Metrical Fixed Point Theory, originating from the 1922 Banach Fixed Point Theorem, is one of the most dynamic areas within Operator Equations Theory. This book aims to discuss the foundational aspects of this theory, focusing on questions of existence, uniqueness, and approximation in operator equations — whether explicit or implicit, anticipative or non-anticipative — across standard, ordered, and relational metric spaces. Key themes include implicit methods for analyzing metrical contractions, factorial techniques for reducing coincidence point problems to standard fixed point ones, homotopical fixed point results in gauge spaces with ordered metric space parameters, and constant class reduction of PPF-dependent fixed point results.
The book is structured into four chapters. Chapter 1 provides an overview of essential preliminary concepts. Chapter 2 delves into various contraction classes within bi-relational, local Branciari, and ordered metric spaces. Chapter 3 applies maximal techniques to address the discussed questions, and Chapter 4 explores additional topics, including contractive-type conditions derived from self and non-self maps. Through this structure, the book offers a comprehensive view of the core aspects and applications of Metrical Fixed Point Theory.
Contents:
- Preliminaries:
- Dependent Choice Principles
- Conv-Cauchy Structures
- Admissible Functions
- Classes of Natural Progressions
- Geometric-Asymptotic Relations
- Topological Structures
- Banach Contractions and Relatives
- Classes of Contractive Maps:
- Anticipative Rhoades Contractions in bi-Relational Metric Spaces
- Functional Contractions in Local Branciari Ordered Metric Spaces
- Matkowski Regular Maps in Ordered Metric Spaces
- Fixed Points via Multistep Type Iterations
- Maximal Techniques:
- Caristi-Kirk Results in Banach Lattices
- Tarski Fixed Point Results over Separable Structures
- Homotopic Metric Interval Maps in Gauge Spaces
- Varia:
- Geometric Functional Contractions in Ordered Quasi-Metric Spaces
- Factorial Jungck Contractions in Ordered Metric Spaces
- Kannan Spectral Contractive Maps in Relational Metric Spaces
- PPF Dependent Fixed Points and the Unexpected Way to Nirvana
- Meir-Keeler Maps in Order Pseudometric Spaces
Readership: Graduates and researchers in metrical fixed point theory and operator equations.
Mihai Turinici is a retired professor from the Faculty of Mathematics at A I Cuza University in Iaşi, Romania. His main research areas include Operator Equations Theory (with a particular focus on Metrical Fixed Point Theory) and Variational Analysis (especially Maximal and Variational Principles).
Metrical Fixed Point Theory, originating from the 1922 Banach Fixed Point Theorem, is one of the most dynamic areas within Operator Equations Theory. This book aims to discuss the foundational aspects of this theory, focusing on questions of existence, uniqueness, and approximation in operator equations — whether explicit or implicit, anticipative or non-anticipative — across standard, ordered, and relational metric spaces. Key themes include implicit methods for analyzing metrical contractions, factorial techniques for reducing coincidence point problems to standard fixed point ones, homotopical fixed point results in gauge spaces with ordered metric space parameters, and constant class reduction of PPF-dependent fixed point results.
The book is structured into four chapters. Chapter 1 provides an overview of essential preliminary concepts. Chapter 2 delves into various contraction classes within bi-relational, local Branciari, and ordered metric spaces. Chapter 3 applies maximal techniques to address the discussed questions, and Chapter 4 explores additional topics, including contractive-type conditions derived from self and non-self maps. Through this structure, the book offers a comprehensive view of the core aspects and applications of Metrical Fixed Point Theory.
Contents:
- Preliminaries:
- Dependent Choice Principles
- Conv-Cauchy Structures
- Admissible Functions
- Classes of Natural Progressions
- Geometric-Asymptotic Relations
- Topological Structures
- Banach Contractions and Relatives
- Classes of Contractive Maps:
- Anticipative Rhoades Contractions in bi-Relational Metric Spaces
- Functional Contractions in Local Branciari Ordered Metric Spaces
- Matkowski Regular Maps in Ordered Metric Spaces
- Fixed Points via Multistep Type Iterations
- Maximal Techniques:
- Caristi-Kirk Results in Banach Lattices
- Tarski Fixed Point Results over Separable Structures
- Homotopic Metric Interval Maps in Gauge Spaces
- Varia:
- Geometric Functional Contractions in Ordered Quasi-Metric Spaces
- Factorial Jungck Contractions in Ordered Metric Spaces
- Kannan Spectral Contractive Maps in Relational Metric Spaces
- PPF Dependent Fixed Points and the Unexpected Way to Nirvana
- Meir-Keeler Maps in Order Pseudometric Spaces
Readership: Graduates and researchers in metrical fixed point theory and operator equations.
Mihai Turinici is a retired professor from the Faculty of Mathematics at A I Cuza University in Iaşi, Romania. His main research areas include Operator Equations Theory (with a particular focus on Metrical Fixed Point Theory) and Variational Analysis (especially Maximal and Variational Principles).
MODERN TOPICS IN METRICAL FIXED POINT THEORY
548
MODERN TOPICS IN METRICAL FIXED POINT THEORY
548
Product Details
| ISBN-13: | 9789819807284 |
|---|---|
| Publisher: | WSPC |
| Publication date: | 02/20/2025 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 548 |
| File size: | 2 MB |