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Fixed Point Theory in Modular Function Spaces / / by Mohamed A. Khamsi, Wojciech M. Kozlowski
| Fixed Point Theory in Modular Function Spaces / / by Mohamed A. Khamsi, Wojciech M. Kozlowski |
| Autore | Khamsi Mohamed A |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015 |
| Descrizione fisica | 1 online resource (251 p.) |
| Disciplina | 510 |
| Soggetto topico |
Operator theory
Functional analysis Operator Theory Functional Analysis |
| ISBN | 3-319-14051-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Fixed Point Theory in Metric Spaces: An Introduction -- Modular Function Spaces -- Geometry of Modular Function Spaces -- Fixed Point Existence Theorems in Modular Function Spaces -- Fixed Point Construction Processes -- Semigroups of Nonlinear Mappings in Modular Function Spaces -- Modular Metric Spaces. |
| Record Nr. | UNINA-9910299773903321 |
Khamsi Mohamed A
|
||
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to metric spaces and fixed point theory [[electronic resource] /] / Mohamed A. Khamsi, William A. Kirk
| An introduction to metric spaces and fixed point theory [[electronic resource] /] / Mohamed A. Khamsi, William A. Kirk |
| Autore | Khamsi Mohamed A |
| Pubbl/distr/stampa | New York, : John Wiley, c2001 |
| Descrizione fisica | 1 online resource (318 p.) |
| Disciplina |
514
514.32 514/.32 |
| Altri autori (Persone) | KirkW. A |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Fixed point theory
Metric spaces |
| ISBN |
1-283-30626-3
9786613306265 1-118-03307-8 1-118-03132-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
An Introduction to Metric Spaces and Fixed Point Theory; Contents; Preface; I Metric Spaces; 1 Introduction; 1.1 The real numbers R; 1.2 Continuous mappings in R; 1.3 The triangle inequality in R; 1.4 The triangle inequality in Rn; 1.5 Brouwer's Fixed Point Theorem; Exercises; 2 Metric Spaces; 2.1 The metric topology; 2.2 Examples of metric spaces; 2.3 Completeness; 2.4 Separability and connectedness; 2.5 Metric convexity and convexity structures; Exercises; 3 Metric Contraction Principles; 3.1 Banach's Contraction Principle; 3.2 Further extensions of Banach's Principle
3.3 The Caristi-Ekeland Principle3.4 Equivalents of the Caristi-Ekeland Principle; 3.5 Set-valued contractions; 3.6 Generalized contractions; Exercises; 4 Hyperconvex Spaces; 4.1 Introduction; 4.2 Hyperconvexity; 4.3 Properties of hyperconvex spaces; 4.4 A fixed point theorem; 4.5 Intersections of hyperconvex spaces; 4.6 Approximate fixed points; 4.7 Isbell's hyperconvex hull; Exercises; 5 ""Normal"" Structures in Metric Spaces; 5.1 A fixed point theorem; 5.2 Structure of the fixed point set; 5.3 Uniform normal structure; 5.4 Uniform relative normal structure; 5.5 Quasi-normal structure 5.6 Stability and normal structure5.7 Ultrametric spaces; 5.8 Fixed point set structure-separable case; Exercises; II Banach Spaces; 6 Banach Spaces: Introduction; 6.1 The definition; 6.2 Convexity; 6.3 l2 revisited; 6.4 The modulus of convexity; 6.5 Uniform convexity of the lp spaces; 6.6 The dual space: Hahn-Banach Theorem; 6.7 The weak and weak* topologies; 6.8 The spaces c, c0, l1 and l(infinity); 6.9 Some more general facts; 6.10 The Schur property and l1; 6.11 More on Schauder bases in Banach spaces; 6.12 Uniform convexity and reflexivity; 6.13 Banach lattices; Exercises 7 Continuous Mappings in Banach Spaces7.1 Introduction; 7.2 Brouwer's Theorem; 7.3 Further comments on Brouwer's Theorem; 7.4 Schauder's Theorem; 7.5 Stability of Schauder's Theorem; 7.6 Banach algebras: Stone Weierstrass Theorem; 7.7 Leray-Schauder degree; 7.8 Condensing mappings; 7.9 Continuous mappings in hyperconvex spaces; Exercises; 8 Metric Fixed Point Theory; 8.1 Contraction mappings; 8.2 Basic theorems for nonexpansive mappings; 8.3 A closer look at l1; 8.4 Stability results in arbitrary spaces; 8.5 The Goebel-Karlovitz Lemma; 8.6 Orthogonal convexity 8.7 Structure of the fixed point set8.8 Asymptotically regular mappings; 8.9 Set-valued mappings; 8.10 Fixed point theory in Banach lattices; Exercises; 9 Banach Space Ultrapowers; 9.1 Finite representability; 9.2 Convergence of ultranets; 9.3 The Banach space ultrapower X; 9.4 Some properties of X; 9.5 Extending mappings to X; 9.6 Some fixed point theorems; 9.7 Asymptotically nonexpansive mappings; 9.8 The demiclosedness principle; 9.9 Uniformly non-creasy spaces; Exercises; Appendix: Set Theory; A.1 Mappings; A.2 Order relations and Zermelo's Theorem A.3 Zorn's Lemma and the Axiom Of Choice |
| Record Nr. | UNINA-9910139576003321 |
|
Khamsi Mohamed A
|
||
| New York, : John Wiley, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to metric spaces and fixed point theory [[electronic resource] /] / Mohamed A. Khamsi, William A. Kirk
| An introduction to metric spaces and fixed point theory [[electronic resource] /] / Mohamed A. Khamsi, William A. Kirk |
| Autore | Khamsi Mohamed A |
| Pubbl/distr/stampa | New York, : John Wiley, c2001 |
| Descrizione fisica | 1 online resource (318 p.) |
| Disciplina |
514
514.32 514/.32 |
| Altri autori (Persone) | KirkW. A |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Fixed point theory
Metric spaces |
| ISBN |
1-283-30626-3
9786613306265 1-118-03307-8 1-118-03132-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
An Introduction to Metric Spaces and Fixed Point Theory; Contents; Preface; I Metric Spaces; 1 Introduction; 1.1 The real numbers R; 1.2 Continuous mappings in R; 1.3 The triangle inequality in R; 1.4 The triangle inequality in Rn; 1.5 Brouwer's Fixed Point Theorem; Exercises; 2 Metric Spaces; 2.1 The metric topology; 2.2 Examples of metric spaces; 2.3 Completeness; 2.4 Separability and connectedness; 2.5 Metric convexity and convexity structures; Exercises; 3 Metric Contraction Principles; 3.1 Banach's Contraction Principle; 3.2 Further extensions of Banach's Principle
3.3 The Caristi-Ekeland Principle3.4 Equivalents of the Caristi-Ekeland Principle; 3.5 Set-valued contractions; 3.6 Generalized contractions; Exercises; 4 Hyperconvex Spaces; 4.1 Introduction; 4.2 Hyperconvexity; 4.3 Properties of hyperconvex spaces; 4.4 A fixed point theorem; 4.5 Intersections of hyperconvex spaces; 4.6 Approximate fixed points; 4.7 Isbell's hyperconvex hull; Exercises; 5 ""Normal"" Structures in Metric Spaces; 5.1 A fixed point theorem; 5.2 Structure of the fixed point set; 5.3 Uniform normal structure; 5.4 Uniform relative normal structure; 5.5 Quasi-normal structure 5.6 Stability and normal structure5.7 Ultrametric spaces; 5.8 Fixed point set structure-separable case; Exercises; II Banach Spaces; 6 Banach Spaces: Introduction; 6.1 The definition; 6.2 Convexity; 6.3 l2 revisited; 6.4 The modulus of convexity; 6.5 Uniform convexity of the lp spaces; 6.6 The dual space: Hahn-Banach Theorem; 6.7 The weak and weak* topologies; 6.8 The spaces c, c0, l1 and l(infinity); 6.9 Some more general facts; 6.10 The Schur property and l1; 6.11 More on Schauder bases in Banach spaces; 6.12 Uniform convexity and reflexivity; 6.13 Banach lattices; Exercises 7 Continuous Mappings in Banach Spaces7.1 Introduction; 7.2 Brouwer's Theorem; 7.3 Further comments on Brouwer's Theorem; 7.4 Schauder's Theorem; 7.5 Stability of Schauder's Theorem; 7.6 Banach algebras: Stone Weierstrass Theorem; 7.7 Leray-Schauder degree; 7.8 Condensing mappings; 7.9 Continuous mappings in hyperconvex spaces; Exercises; 8 Metric Fixed Point Theory; 8.1 Contraction mappings; 8.2 Basic theorems for nonexpansive mappings; 8.3 A closer look at l1; 8.4 Stability results in arbitrary spaces; 8.5 The Goebel-Karlovitz Lemma; 8.6 Orthogonal convexity 8.7 Structure of the fixed point set8.8 Asymptotically regular mappings; 8.9 Set-valued mappings; 8.10 Fixed point theory in Banach lattices; Exercises; 9 Banach Space Ultrapowers; 9.1 Finite representability; 9.2 Convergence of ultranets; 9.3 The Banach space ultrapower X; 9.4 Some properties of X; 9.5 Extending mappings to X; 9.6 Some fixed point theorems; 9.7 Asymptotically nonexpansive mappings; 9.8 The demiclosedness principle; 9.9 Uniformly non-creasy spaces; Exercises; Appendix: Set Theory; A.1 Mappings; A.2 Order relations and Zermelo's Theorem A.3 Zorn's Lemma and the Axiom Of Choice |
| Record Nr. | UNINA-9910830306203321 |
|
Khamsi Mohamed A
|
||
| New York, : John Wiley, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to metric spaces and fixed point theory / / Mohamed A. Khamsi, William A. Kirk
| An introduction to metric spaces and fixed point theory / / Mohamed A. Khamsi, William A. Kirk |
| Autore | Khamsi Mohamed A |
| Pubbl/distr/stampa | New York, : John Wiley, c2001 |
| Descrizione fisica | 1 online resource (318 p.) |
| Disciplina | 514/.32 |
| Altri autori (Persone) | KirkW. A |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Fixed point theory
Metric spaces |
| ISBN |
9786613306265
9781283306263 1283306263 9781118033074 1118033078 9781118031322 1118031326 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
An Introduction to Metric Spaces and Fixed Point Theory; Contents; Preface; I Metric Spaces; 1 Introduction; 1.1 The real numbers R; 1.2 Continuous mappings in R; 1.3 The triangle inequality in R; 1.4 The triangle inequality in Rn; 1.5 Brouwer's Fixed Point Theorem; Exercises; 2 Metric Spaces; 2.1 The metric topology; 2.2 Examples of metric spaces; 2.3 Completeness; 2.4 Separability and connectedness; 2.5 Metric convexity and convexity structures; Exercises; 3 Metric Contraction Principles; 3.1 Banach's Contraction Principle; 3.2 Further extensions of Banach's Principle
3.3 The Caristi-Ekeland Principle3.4 Equivalents of the Caristi-Ekeland Principle; 3.5 Set-valued contractions; 3.6 Generalized contractions; Exercises; 4 Hyperconvex Spaces; 4.1 Introduction; 4.2 Hyperconvexity; 4.3 Properties of hyperconvex spaces; 4.4 A fixed point theorem; 4.5 Intersections of hyperconvex spaces; 4.6 Approximate fixed points; 4.7 Isbell's hyperconvex hull; Exercises; 5 ""Normal"" Structures in Metric Spaces; 5.1 A fixed point theorem; 5.2 Structure of the fixed point set; 5.3 Uniform normal structure; 5.4 Uniform relative normal structure; 5.5 Quasi-normal structure 5.6 Stability and normal structure5.7 Ultrametric spaces; 5.8 Fixed point set structure-separable case; Exercises; II Banach Spaces; 6 Banach Spaces: Introduction; 6.1 The definition; 6.2 Convexity; 6.3 l2 revisited; 6.4 The modulus of convexity; 6.5 Uniform convexity of the lp spaces; 6.6 The dual space: Hahn-Banach Theorem; 6.7 The weak and weak* topologies; 6.8 The spaces c, c0, l1 and l(infinity); 6.9 Some more general facts; 6.10 The Schur property and l1; 6.11 More on Schauder bases in Banach spaces; 6.12 Uniform convexity and reflexivity; 6.13 Banach lattices; Exercises 7 Continuous Mappings in Banach Spaces7.1 Introduction; 7.2 Brouwer's Theorem; 7.3 Further comments on Brouwer's Theorem; 7.4 Schauder's Theorem; 7.5 Stability of Schauder's Theorem; 7.6 Banach algebras: Stone Weierstrass Theorem; 7.7 Leray-Schauder degree; 7.8 Condensing mappings; 7.9 Continuous mappings in hyperconvex spaces; Exercises; 8 Metric Fixed Point Theory; 8.1 Contraction mappings; 8.2 Basic theorems for nonexpansive mappings; 8.3 A closer look at l1; 8.4 Stability results in arbitrary spaces; 8.5 The Goebel-Karlovitz Lemma; 8.6 Orthogonal convexity 8.7 Structure of the fixed point set8.8 Asymptotically regular mappings; 8.9 Set-valued mappings; 8.10 Fixed point theory in Banach lattices; Exercises; 9 Banach Space Ultrapowers; 9.1 Finite representability; 9.2 Convergence of ultranets; 9.3 The Banach space ultrapower X; 9.4 Some properties of X; 9.5 Extending mappings to X; 9.6 Some fixed point theorems; 9.7 Asymptotically nonexpansive mappings; 9.8 The demiclosedness principle; 9.9 Uniformly non-creasy spaces; Exercises; Appendix: Set Theory; A.1 Mappings; A.2 Order relations and Zermelo's Theorem A.3 Zorn's Lemma and the Axiom Of Choice |
| Record Nr. | UNINA-9911019524403321 |
|
Khamsi Mohamed A
|
||
| New York, : John Wiley, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||