Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Analytic capacity and measure / / J. Garnett
| Analytic capacity and measure / / J. Garnett |
| Autore | Garnett J. |
| Edizione | [1st ed. 1972.] |
| Pubbl/distr/stampa | Berlin : , : Springer, , [1972] |
| Descrizione fisica | 1 online resource (IV, 141 p.) |
| Disciplina | 515.9 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Analytic functions
Approximation theory - Data processing |
| ISBN | 3-540-38003-5 |
| Classificazione | 30C85 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Analytic capacity -- The cauchy transform -- Hausdorff measure -- Some examples -- Applications to approximation. |
| Record Nr. | UNISA-996466854803316 |
Garnett J.
|
||
| Berlin : , : Springer, , [1972] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Approximation theory, sequence spaces and applications / / S. A. Mohiuddine, Bipan Hazarika, and Hemant Kumar Nashine
| Approximation theory, sequence spaces and applications / / S. A. Mohiuddine, Bipan Hazarika, and Hemant Kumar Nashine |
| Autore | Mohiuddine S. A. |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (277 pages) |
| Disciplina | 511.4 |
| Collana | Industrial and Applied Mathematics |
| Soggetto topico |
Approximation theory
Approximation theory - Data processing Teoria de l'aproximació Processament de dades |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-6116-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- About the Editors -- 1 Topology on Geometric Sequence Spaces -- 1.1 Introduction -- 1.1.1 α-Generator and Geometric Complex Field -- 1.1.2 Some Useful Relations Between Geometric Operations and Ordinary Arithmetic Operations -- 1.1.3 G-Limit -- 1.1.4 G-Continuity -- 1.2 Geometric Vector Spaces -- 1.2.1 Geometric Vector Space -- 1.2.2 Dual System -- 1.3 Topology on Geometric Sequence Spaces -- 1.3.1 Normal Topology -- 1.3.2 Perfect Sequence Space -- 1.3.3 Simple Space -- 1.3.4 Symmetric Sequence Spaces -- References -- 2 Composition Operators on Second-Order Cesàro Function Spaces -- 2.1 Introduction -- 2.2 Examining the Boundedness -- 2.3 Compactness and Essential Norm of Composition Operators -- 2.4 Fredholm Composition Operators -- 2.5 Conclusion -- References -- 3 Generalized Deferred Statistical Convergence -- 3.1 Definitions and Preliminaries -- 3.2 Deferred Statistical Convergence of Order αβ -- 3.3 Strong s-Deferred Cesàro Summability of Order αβ -- 3.4 Inclusion Theorems -- 3.5 Special Cases -- References -- 4 Approximation by Generalized Lupaş-Pǎltǎnea Operators -- 4.1 Introduction -- 4.2 Basic Results -- 4.3 Main Results -- 4.3.1 Weighted Approximation -- 4.3.2 Quantitative Voronoskaja-Type Approximation Theorem -- 4.3.3 Grüss Voronovskaya-Type Theorem -- 4.3.4 Approximation Properties of DBV[0,infty) -- References -- 5 Zachary Spaces mathcalZp[mathbbRinfty] and Separable Banach Spaces -- 5.1 Introduction -- 5.1.1 Preliminaries -- 5.1.2 Basis for a Banach Spaces -- 5.2 Space of Functions of Bounded Mean Oscillation (BMO[mathbbRIinfty]) -- 5.3 Zachary Space mathcalZp[mathbbRIinfty] -- 5.4 Zachary Space mathcalZp[mathfrakB], Where mathfrakB is Separable Banach Space -- References -- 6 New Generalization of the Power Summability Methods for Dunkl Generalization of Szász Operators via q-Calculus.
6.1 Introduction -- 6.2 Dunkl Generalization of the Szász Operators Obtained by q-Calculus -- 6.3 Preliminary Results -- 6.4 Direct Estimates -- 6.5 Weighted Approximation -- 6.6 Statistical Approximation Properties for Dunkl Generalization of Szász Operators via q-Calculus -- 6.7 Rate of Convergence of the Dunkl Generalization of Szász Operators via q-Calculus -- 6.8 Conclusion -- References -- 7 Approximation by Generalized Szász-Jakimovski-Leviatan Type Operators -- 7.1 Introduction -- 7.2 Construction of Operators and Estimation of Moments -- 7.3 Approximation in Weighted Spaces -- 7.4 Some Direct Approximation Theorems -- 7.5 A-Statistical Convergence -- 7.6 Conclusion -- References -- 8 On Approximation of Signals -- 8.1 Introduction -- 8.2 Known Results -- 8.3 Main Theorems -- 8.4 Lemmas -- 8.5 Proof of the Lemmas -- 8.6 Proof of Main Theorems -- 8.7 Conclusion -- References -- 9 Numerical Solution for Nonlinear Problems -- 9.1 Introduction -- 9.2 Introducing Some Nonlinear Functional and Fractional Equations -- 9.3 A Coupled Semi-analytic Method to Find the Solution of Equation (9.1) -- 9.3.1 Constructing Some Iterative Algorithms to Approximate the Solution of Equations (9.2)-(9.5) -- 9.4 Convergence of the Algorithms -- 9.5 Constructing an Iterative Algorithm by Sinc Function -- 9.5.1 One-Dimensional Functional Integral Equation -- 9.5.2 Convergence of Algorithm (9.62) -- 9.5.3 Two-Dimensional Functional Integral Equation -- References -- 10 Szász-Type Operators Involving q-Appell Polynomials -- 10.1 Introduction -- 10.2 Construction of the Operators and Basic Estimates -- 10.3 Some Basic Results -- 10.4 Pointwise Approximation Results -- 10.5 Weighted Approximation -- 10.6 A-Statistical Approximation -- References -- 11 Commutants of the Infinite Hilbert Operators -- 11.1 Introduction -- 11.2 Main Results. 11.3 Norm of Operators on Sequence Spaces Φn(p) and Ψn(p) -- References -- 12 On Complex Uncertain Sequences Defined by Orlicz Function -- 12.1 Introduction -- 12.2 Preliminaries -- 12.3 Complex Uncertain Sequence Spaces -- 12.4 Statistical Convergence of Complex Uncertain Sequences -- 12.5 Complex Uncertain Sequence Spaces Defined by Orlicz Function -- 12.6 Statistical Convergence of Complex Uncertain Sequences Defined by Orlicz Function -- 12.7 On Paranormed Type p-Absolutely Summable Uncertain Sequence Spaces Defined by Orlicz Functions -- 12.8 Lacunary Convergence Concepts of Complex Uncertain Sequences with Respect to Orlicz Function -- 12.9 Conclusion -- References -- 13 Ulam-Hyers Stability of Mixed Type Functional Equation Deriving From Additive and Quadratic Mappings in Intuitionistic Random Normed Spaces -- 13.1 Introduction -- 13.2 Preliminaries -- 13.3 Ulam-Hyers Stability for Odd Case -- 13.4 Ulam-Hyers Stability for Even Case -- 13.5 Ulam-Hyers Stability for Mixed Case -- 13.6 Conclusion -- References -- 14 A Study on q-Euler Difference Sequence Spaces -- 14.1 Introduction, Preliminaries, and Notations -- 14.1.1 Euler Matrix of Order 1 and Sequence Spaces -- 14.1.2 q-Calculus -- 14.2 q-Euler Difference Sequence Spaces -- 14.3 Alpha-, Beta-, and Gamma-Duals of q-Euler Difference Sequence Spaces -- 14.4 Matrix Transformations -- 14.5 Compact Operators and Hausdorff Measure of Non-compactness (Hmnc) -- References. |
| Record Nr. | UNISA-996503551903316 |
|
Mohiuddine S. A.
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Geometric approximation theory / / Alexey R. Alimov and Igor' G. Tsar'kov
| Geometric approximation theory / / Alexey R. Alimov and Igor' G. Tsar'kov |
| Autore | Alimov Alexey |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (523 pages) |
| Disciplina | 511.4 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Teoria de l'aproximació
Sistemes de Txebixov Approximation theory Approximation theory - Data processing |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-90951-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Main Notation, Definitions, Auxiliary Results, and Examples -- 1.1 Main Definitions of Geometric Approximation Theory -- 1.2 Preliminaries and Some Facts from Functional Analysis -- 1.3 Elementary Results on Best Approximation. Strictly Convex Spaces. Approximation by Subspaces and Hyperplanes -- 2 Chebyshev Alternation Theorem. Haar's and Mairhuber's Theorems -- 2.1 Chebyshev's and de la Vallée Poussin's Theorems -- 2.2 Solarity and Alternant -- 2.3 Haar's Theorem. Strong Uniqueness of Best Approximation -- 2.4 A Short Note on Extremal Signatures -- 2.5 Mairhuber's Theorem -- 2.6 Approximation of Continuous Functions by Finite-Dimensional Subspaces in the L1-Metric -- 2.7 Remez's Algorithm for Construction of a Polynomials of Near-Best Approximation -- 3 Best Approximation in Euclidean Spaces -- 3.1 Approximation by Convex Sets. Kolmogorov Criterion for a Nearest Element. Deutsch's Lemma -- 3.2 Phelps's Theorem on the Lipschitz Continuity of the Metric Projection onto Chebyshev Sets -- 3.3 Best Least-Squares Polynomial Approximation. Orthogonal Polynomials -- 4 Existence. Compact, Boundedly Compact, Approximatively Compact, and τ-Compact Sets. Continuity of the Metric Projection -- 4.1 Boundedly Compact and Approximatively Compact Sets -- 4.2 Existence of Best Approximation -- 4.3 Approximative τ-Compactness with Respect to Regular τ-Convergence -- 4.3.1 Applications in C[a,b] -- 4.3.2 Applications in Lp -- 5 Characterization of Best Approximation and Solar Properties of Sets -- 5.1 Characterization of an Element of Best Approximation -- 5.2 Suns and the Kolmogorov Criterion for a Nearest Element. Local and Global Best Approximation. Unimodal Sets (LG-Sets) -- 5.3 Kolmogorov Criterion in the Space C(Q) -- 5.4 Continuity of the Metric Projection onto Chebyshev Sets.
5.5 Differentiability of the Distance Function -- 5.6 Relation of Geometric Approximation Theory to Geometric Optics -- 6 Convexity of Chebyshev Sets and Suns -- 6.1 Convexity of Suns -- 6.2 Convexity of Chebyshev Sets in mathbbRn -- 6.2.1 Berdyshev-Klee-Vlasov's proof -- 6.2.2 Asplund's Proof -- 6.2.3 Konyagin's Proof -- 6.2.4 Vlasov's Proof -- 6.2.5 Brosowski's Proof -- 6.3 The Klee Cavern -- 6.4 Johnson's Example of a Nonconvex Chebyshev Set in an Incomplete Pre-Hilbert Space -- 7 Connectedness and Approximative Properties of Sets. Stability of the Metric Projection and Its Relation to Other Approximative Properties -- 7.1 Classes of Connectedness of Sets -- 7.2 Connectedness of Suns -- 7.3 Dunham's Example of a Disconnected Chebyshev Set with Isolated Point -- 7.4 Klee's Example of a Discrete Chebyshev Set -- 7.5 Koshcheev's Example of a Disconnected Sun -- 7.6 Radial Continuity of the Metric Projection. B-Connectedness of Approximatively Compact Chebyshev Suns -- 7.7 Spans, Segments. Menger Connectedness, and Monotone Path-Connectedness -- 7.7.1 The Banach-Mazur Hull -- 7.7.2 Segments and Spans in Normed Linear Spaces -- 7.7.3 Monotone Path-Connectedness -- 7.8 Continuous and Semicontinuous Selections of Metric Projection. Relation to Solarity and Proximinality of Sets -- 7.9 Suns, Unimodal Sets, Moons, and ORL-Continuity. Brosowski-Wegmann-connectedness -- 7.10 Solarity of the Set of Generalized Rational Fractions -- 7.11 Approximative Properties of Sets Lying in a Subspace -- 7.12 Approximation by Products -- 8 Existence of Chebyshev Subspaces -- 8.1 Chebyshev Subspaces in Finite-Dimensional Spaces -- 8.2 Chebyshev Subspaces in Infinite-Dimensional Spaces -- 8.3 Finite-Dimensional Chebyshev Subspaces in L1(µ). 9 Efimov-Stechkin Spaces. Uniform Convexity and Uniform Smoothness. Uniqueness and Strong Uniqueness of Best Approximation in Uniformly Convex Spaces -- 9.1 Efimov-Stechkin Spaces -- 9.2 Uniformly Convex Spaces -- 9.3 Uniqueness of Best Approximation by Convex Closed Sets … -- 9.4 Strong Uniqueness in Uniformly Convex Spaces -- 9.5 Uniformly Smooth Spaces -- 10 Solarity of Chebyshev Sets -- 10.1 Solarity of Boundedly Compact Chebyshev Sets -- 10.2 Relations Between Classes of Suns -- 10.3 Solarity of Chebyshev Sets -- 10.3.1 Solarity of Chebyshev Sets with Continuous Metric Projection -- 10.4 Solarity and Structural Properties of Sets -- 10.4.1 Solarity of Monotone Path-Connected Chebyshev Sets -- 10.4.2 Acyclicity and Cell-Likeness of Sets -- 10.4.3 Solarity of Boundedly Compact P-Acyclic Sets -- 11 Rational Approximation -- 11.1 Existence of a Best Rational Approximation -- 11.2 Characterization of Best Rational Approximation in the Space C[a,b] -- 11.3 Rational Lp-Approximation -- 11.4 Existence of Best Approximation by Generalized Rational Fractions -- 11.5 Characterization of Best Generalized Rational Approximation -- 11.6 Uniqueness of General Rational Approximation -- 11.7 Continuity of the Best Rational Approximation Operator -- 11.8 Notes on Algorithms of Rational Approximations -- 12 Haar Cones and Varisolvency -- 12.1 Properties of Haar Cones. Uniqueness … -- 12.2 Alternation Theorem for Haar Cones -- 12.3 Varisolvency -- 12.3.1 Uniqueness of Best Approximation by Varisolvent Sets -- 12.3.2 Regular and Singular Points in Approximation by Varisolvent Sets -- 13 Approximation of Vector-Valued Functions -- 13.1 Approximation of Abstract Functions. Interpolation and Uniqueness -- 13.2 Uniqueness of Best Approximation in the Mean for Vector-Valued Functions -- 13.3 On the Haar Condition for Systems of Vector-Valued Functions. 13.4 Approximation of Vector-Valued Functions by Polynomials -- 13.5 Some Applications of Vector-Valued Approximation -- 14 The Jung Constant -- 14.1 Definition of the Jung Constant -- 14.2 The Measure of Nonconvexity of a Space and the Jung Constant -- 14.3 The Jung Constant and Fixed Points of Condensing and Nonexpansive Maps -- 14.4 On an Approximate Solution of the Equation f(x)=x -- 14.5 On the Jung Constant of the Space ell1n -- 14.6 The Jung Constant and the Jackson Constant -- 14.7 The Relative Jung Constant -- 14.8 The Jung Constant of a Pair of Spaces -- 14.9 Some Remarks on Intersections of Convex Sets. Relation to the Jung Constant -- 15 Chebyshev Centre of a Set. The Problem of Simultaneous Approximation of a Class by a Singleton Set -- 15.1 Chebyshev Centre of a Set -- 15.2 Chebyshev Centres and Spans -- 15.3 Chebyshev Centre in the Space C(Q) -- 15.4 Existence of a Chebyshev Centre in Normed Spaces -- 15.4.1 Quasi-uniform Convexity and Existence of Chebyshev Centres -- 15.5 Uniqueness of a Chebyshev Centre -- 15.5.1 Uniqueness of a Chebyshev Centre of a Compact Set -- 15.5.2 Uniqueness of a Chebyshev Centre of a Bounded Set -- 15.6 Stability of the Chebyshev-Centre Map -- 15.6.1 Stability of the Chebyshev-Centre Map in Arbitrary Normed Spaces -- 15.6.2 Quasi-uniform Convexity and Stability of the Chebyshev-Centre Map -- 15.6.3 Stability of the Chebyshev-Centre Map in Finite-Dimensional Polyhedral Spaces -- 15.6.4 Stability of the Chebyshev-Centre Map in C(Q)-Spaces -- 15.6.5 Stability of the Chebyshev-Centre Map in Hilbert and Uniformly Convex Spaces -- 15.6.6 Stability of the Self-Chebyshev-Centre Map -- 15.6.7 Upper Semicontinuity of the Chebyshev-Centre Map and the Chebyshev-Near-Centre Map -- 15.6.8 Lipschitz Selection of the Chebyshev-Centre Map -- 15.6.9 Discontinuity of the Chebyshev-Centre Map. 15.7 Characterization of a Chebyshev Centre. Decomposition Theorem -- 15.8 Chebyshev Centres That Are Not Farthest Points -- 15.9 Smooth and Continuous Selections of the Chebyshev-Near-Centre Map -- 15.10 Algorithms and Applied Problems Connected with Chebyshev Centres -- 16 Width. Approximation by a Family of Sets -- 16.1 Problems in Recovery and Approximation Leading to Widths -- 16.2 Definitions of Widths -- 16.3 Fundamental Properties of Widths -- 16.4 Evaluation of Widths of ellp-Ellipsoids -- 16.5 Dranishnikov-Shchepin Widths and Their Relation to the CE-Problem -- 16.6 Bernstein Widths in the Spaces Linfty[0,1] -- 16.7 Widths of Function Classes -- 16.7.1 Definition of the Information Width -- 16.7.2 Estimates for Information Kolmogorov Widths -- 16.7.3 Some Exact Inequalities Between Widths. Projection Constants -- 16.7.4 Some Order Estimates and Duality of Information Width -- 16.7.5 Some Order Estimates for Information Kolmogorov Widths of Finite-Dimensional Balls -- 16.7.6 Order Estimates for Information Kolmogorov Widths of Function Classes -- 16.8 Relation Between the Jung Constant and Widths of Sets -- 16.9 Sequence of Best Approximations -- 17 Approximative Properties of Arbitrary Sets in Normed Linear Spaces. Almost Chebyshev Sets and Sets of Almost Uniqueness -- 17.1 Approximative Properties of Arbitrary Sets -- 17.2 Sets in Strictly Convex Spaces -- 17.3 Constructive Characteristics of Spaces -- 17.4 Sets in Locally Uniformly Convex Spaces -- 17.5 Sets in Uniformly Convex Spaces -- 17.6 Examples -- 17.7 Density and Category Properties of the Sets E(M), AC(M), and T(M) -- 17.8 Category Properties of the Set U(M) -- 17.9 Other Characteristics for the Size of Approximatively Defined Sets -- 17.10 The Farthest-Point Problem -- 17.11 Classes of Small Sets (Zk) -- 17.12 Contingent. 17.13 Zajíček-Smallness of the Classes of Sets R(M) and R*(M). |
| Record Nr. | UNISA-996466566103316 |
|
Alimov Alexey
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Geometric approximation theory / / Alexey R. Alimov and Igor' G. Tsar'kov
| Geometric approximation theory / / Alexey R. Alimov and Igor' G. Tsar'kov |
| Autore | Alimov Alexey |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (523 pages) |
| Disciplina | 511.4 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Teoria de l'aproximació
Sistemes de Txebixov Approximation theory Approximation theory - Data processing |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-90951-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Main Notation, Definitions, Auxiliary Results, and Examples -- 1.1 Main Definitions of Geometric Approximation Theory -- 1.2 Preliminaries and Some Facts from Functional Analysis -- 1.3 Elementary Results on Best Approximation. Strictly Convex Spaces. Approximation by Subspaces and Hyperplanes -- 2 Chebyshev Alternation Theorem. Haar's and Mairhuber's Theorems -- 2.1 Chebyshev's and de la Vallée Poussin's Theorems -- 2.2 Solarity and Alternant -- 2.3 Haar's Theorem. Strong Uniqueness of Best Approximation -- 2.4 A Short Note on Extremal Signatures -- 2.5 Mairhuber's Theorem -- 2.6 Approximation of Continuous Functions by Finite-Dimensional Subspaces in the L1-Metric -- 2.7 Remez's Algorithm for Construction of a Polynomials of Near-Best Approximation -- 3 Best Approximation in Euclidean Spaces -- 3.1 Approximation by Convex Sets. Kolmogorov Criterion for a Nearest Element. Deutsch's Lemma -- 3.2 Phelps's Theorem on the Lipschitz Continuity of the Metric Projection onto Chebyshev Sets -- 3.3 Best Least-Squares Polynomial Approximation. Orthogonal Polynomials -- 4 Existence. Compact, Boundedly Compact, Approximatively Compact, and τ-Compact Sets. Continuity of the Metric Projection -- 4.1 Boundedly Compact and Approximatively Compact Sets -- 4.2 Existence of Best Approximation -- 4.3 Approximative τ-Compactness with Respect to Regular τ-Convergence -- 4.3.1 Applications in C[a,b] -- 4.3.2 Applications in Lp -- 5 Characterization of Best Approximation and Solar Properties of Sets -- 5.1 Characterization of an Element of Best Approximation -- 5.2 Suns and the Kolmogorov Criterion for a Nearest Element. Local and Global Best Approximation. Unimodal Sets (LG-Sets) -- 5.3 Kolmogorov Criterion in the Space C(Q) -- 5.4 Continuity of the Metric Projection onto Chebyshev Sets.
5.5 Differentiability of the Distance Function -- 5.6 Relation of Geometric Approximation Theory to Geometric Optics -- 6 Convexity of Chebyshev Sets and Suns -- 6.1 Convexity of Suns -- 6.2 Convexity of Chebyshev Sets in mathbbRn -- 6.2.1 Berdyshev-Klee-Vlasov's proof -- 6.2.2 Asplund's Proof -- 6.2.3 Konyagin's Proof -- 6.2.4 Vlasov's Proof -- 6.2.5 Brosowski's Proof -- 6.3 The Klee Cavern -- 6.4 Johnson's Example of a Nonconvex Chebyshev Set in an Incomplete Pre-Hilbert Space -- 7 Connectedness and Approximative Properties of Sets. Stability of the Metric Projection and Its Relation to Other Approximative Properties -- 7.1 Classes of Connectedness of Sets -- 7.2 Connectedness of Suns -- 7.3 Dunham's Example of a Disconnected Chebyshev Set with Isolated Point -- 7.4 Klee's Example of a Discrete Chebyshev Set -- 7.5 Koshcheev's Example of a Disconnected Sun -- 7.6 Radial Continuity of the Metric Projection. B-Connectedness of Approximatively Compact Chebyshev Suns -- 7.7 Spans, Segments. Menger Connectedness, and Monotone Path-Connectedness -- 7.7.1 The Banach-Mazur Hull -- 7.7.2 Segments and Spans in Normed Linear Spaces -- 7.7.3 Monotone Path-Connectedness -- 7.8 Continuous and Semicontinuous Selections of Metric Projection. Relation to Solarity and Proximinality of Sets -- 7.9 Suns, Unimodal Sets, Moons, and ORL-Continuity. Brosowski-Wegmann-connectedness -- 7.10 Solarity of the Set of Generalized Rational Fractions -- 7.11 Approximative Properties of Sets Lying in a Subspace -- 7.12 Approximation by Products -- 8 Existence of Chebyshev Subspaces -- 8.1 Chebyshev Subspaces in Finite-Dimensional Spaces -- 8.2 Chebyshev Subspaces in Infinite-Dimensional Spaces -- 8.3 Finite-Dimensional Chebyshev Subspaces in L1(µ). 9 Efimov-Stechkin Spaces. Uniform Convexity and Uniform Smoothness. Uniqueness and Strong Uniqueness of Best Approximation in Uniformly Convex Spaces -- 9.1 Efimov-Stechkin Spaces -- 9.2 Uniformly Convex Spaces -- 9.3 Uniqueness of Best Approximation by Convex Closed Sets … -- 9.4 Strong Uniqueness in Uniformly Convex Spaces -- 9.5 Uniformly Smooth Spaces -- 10 Solarity of Chebyshev Sets -- 10.1 Solarity of Boundedly Compact Chebyshev Sets -- 10.2 Relations Between Classes of Suns -- 10.3 Solarity of Chebyshev Sets -- 10.3.1 Solarity of Chebyshev Sets with Continuous Metric Projection -- 10.4 Solarity and Structural Properties of Sets -- 10.4.1 Solarity of Monotone Path-Connected Chebyshev Sets -- 10.4.2 Acyclicity and Cell-Likeness of Sets -- 10.4.3 Solarity of Boundedly Compact P-Acyclic Sets -- 11 Rational Approximation -- 11.1 Existence of a Best Rational Approximation -- 11.2 Characterization of Best Rational Approximation in the Space C[a,b] -- 11.3 Rational Lp-Approximation -- 11.4 Existence of Best Approximation by Generalized Rational Fractions -- 11.5 Characterization of Best Generalized Rational Approximation -- 11.6 Uniqueness of General Rational Approximation -- 11.7 Continuity of the Best Rational Approximation Operator -- 11.8 Notes on Algorithms of Rational Approximations -- 12 Haar Cones and Varisolvency -- 12.1 Properties of Haar Cones. Uniqueness … -- 12.2 Alternation Theorem for Haar Cones -- 12.3 Varisolvency -- 12.3.1 Uniqueness of Best Approximation by Varisolvent Sets -- 12.3.2 Regular and Singular Points in Approximation by Varisolvent Sets -- 13 Approximation of Vector-Valued Functions -- 13.1 Approximation of Abstract Functions. Interpolation and Uniqueness -- 13.2 Uniqueness of Best Approximation in the Mean for Vector-Valued Functions -- 13.3 On the Haar Condition for Systems of Vector-Valued Functions. 13.4 Approximation of Vector-Valued Functions by Polynomials -- 13.5 Some Applications of Vector-Valued Approximation -- 14 The Jung Constant -- 14.1 Definition of the Jung Constant -- 14.2 The Measure of Nonconvexity of a Space and the Jung Constant -- 14.3 The Jung Constant and Fixed Points of Condensing and Nonexpansive Maps -- 14.4 On an Approximate Solution of the Equation f(x)=x -- 14.5 On the Jung Constant of the Space ell1n -- 14.6 The Jung Constant and the Jackson Constant -- 14.7 The Relative Jung Constant -- 14.8 The Jung Constant of a Pair of Spaces -- 14.9 Some Remarks on Intersections of Convex Sets. Relation to the Jung Constant -- 15 Chebyshev Centre of a Set. The Problem of Simultaneous Approximation of a Class by a Singleton Set -- 15.1 Chebyshev Centre of a Set -- 15.2 Chebyshev Centres and Spans -- 15.3 Chebyshev Centre in the Space C(Q) -- 15.4 Existence of a Chebyshev Centre in Normed Spaces -- 15.4.1 Quasi-uniform Convexity and Existence of Chebyshev Centres -- 15.5 Uniqueness of a Chebyshev Centre -- 15.5.1 Uniqueness of a Chebyshev Centre of a Compact Set -- 15.5.2 Uniqueness of a Chebyshev Centre of a Bounded Set -- 15.6 Stability of the Chebyshev-Centre Map -- 15.6.1 Stability of the Chebyshev-Centre Map in Arbitrary Normed Spaces -- 15.6.2 Quasi-uniform Convexity and Stability of the Chebyshev-Centre Map -- 15.6.3 Stability of the Chebyshev-Centre Map in Finite-Dimensional Polyhedral Spaces -- 15.6.4 Stability of the Chebyshev-Centre Map in C(Q)-Spaces -- 15.6.5 Stability of the Chebyshev-Centre Map in Hilbert and Uniformly Convex Spaces -- 15.6.6 Stability of the Self-Chebyshev-Centre Map -- 15.6.7 Upper Semicontinuity of the Chebyshev-Centre Map and the Chebyshev-Near-Centre Map -- 15.6.8 Lipschitz Selection of the Chebyshev-Centre Map -- 15.6.9 Discontinuity of the Chebyshev-Centre Map. 15.7 Characterization of a Chebyshev Centre. Decomposition Theorem -- 15.8 Chebyshev Centres That Are Not Farthest Points -- 15.9 Smooth and Continuous Selections of the Chebyshev-Near-Centre Map -- 15.10 Algorithms and Applied Problems Connected with Chebyshev Centres -- 16 Width. Approximation by a Family of Sets -- 16.1 Problems in Recovery and Approximation Leading to Widths -- 16.2 Definitions of Widths -- 16.3 Fundamental Properties of Widths -- 16.4 Evaluation of Widths of ellp-Ellipsoids -- 16.5 Dranishnikov-Shchepin Widths and Their Relation to the CE-Problem -- 16.6 Bernstein Widths in the Spaces Linfty[0,1] -- 16.7 Widths of Function Classes -- 16.7.1 Definition of the Information Width -- 16.7.2 Estimates for Information Kolmogorov Widths -- 16.7.3 Some Exact Inequalities Between Widths. Projection Constants -- 16.7.4 Some Order Estimates and Duality of Information Width -- 16.7.5 Some Order Estimates for Information Kolmogorov Widths of Finite-Dimensional Balls -- 16.7.6 Order Estimates for Information Kolmogorov Widths of Function Classes -- 16.8 Relation Between the Jung Constant and Widths of Sets -- 16.9 Sequence of Best Approximations -- 17 Approximative Properties of Arbitrary Sets in Normed Linear Spaces. Almost Chebyshev Sets and Sets of Almost Uniqueness -- 17.1 Approximative Properties of Arbitrary Sets -- 17.2 Sets in Strictly Convex Spaces -- 17.3 Constructive Characteristics of Spaces -- 17.4 Sets in Locally Uniformly Convex Spaces -- 17.5 Sets in Uniformly Convex Spaces -- 17.6 Examples -- 17.7 Density and Category Properties of the Sets E(M), AC(M), and T(M) -- 17.8 Category Properties of the Set U(M) -- 17.9 Other Characteristics for the Size of Approximatively Defined Sets -- 17.10 The Farthest-Point Problem -- 17.11 Classes of Small Sets (Zk) -- 17.12 Contingent. 17.13 Zajíček-Smallness of the Classes of Sets R(M) and R*(M). |
| Record Nr. | UNINA-9910556887903321 |
|
Alimov Alexey
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
