Approximation theory, sequence spaces and applications / / S. A. Mohiuddine, Bipan Hazarika, and Hemant Kumar Nashine

• Record Nr.: UNISA996503551903316
• Autore: Mohiuddine S. A.
• Pubbl/distr/stampa: Singapore : , : Springer, , [2022]; ©2022
• ISBN: 981-19-6116-6
• Descrizione fisica: 1 online resource (277 pages)
• Collana: Industrial and Applied Mathematics
• Disciplina: 511.4
• Soggetti: Approximation theory; Approximation theory - Data processing; Teoria de l'aproximació; Processament de dades; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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.