This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
Author(s): Erdal Karapinar, Ravi P. Agarwal
Series: Synthesis Lectures on Mathematics & Statistics
Publisher: Springer
Year: 2022
Language: English
Pages: 140
City: Cham
Preface
Contents
Acronyms
Part I Fixed Point Theorems in the Framework of Metric Spaces
1 Introduction
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2 Metric Spaces
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2.1 Basic Topological Properties of the Metric Spaces
2.2 Connection Between the Normed Spaces and Metric Spaces
2.3 Some Interesting Auxiliary Functions
2.4 Bessage, Janos and Picard Operators
3 Metric Fixed Point Theory
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3.1 Banach Contraction Mapping Principle
3.2 Further Consequences of Banach Fixed Point Theorem
3.2.1 Linear Extensions of Banach Contraction Principle
3.2.2 Nonlinear Extensions of Banach Contraction Principle
3.3 Locally Contractive Mappings and Related Fixed Point Results
3.4 Discussion on the Mappings Whose Iteration form a Contraction
3.5 Extension on Compact Metric Spaces
3.6 Nonunique Fixed Point Theorems
3.7 Fixed Point Results via Admissible Mappings
3.7.1 Standard Fixed Point Theorems
3.7.2 Fixed Point Theorems on Metric Spaces Endowed with a Partial Order
3.7.3 Fixed Point Theorems for Cyclic Contractive Mappings
3.8 Fixed Point Results via Simulation Functions
3.8.1 Immediate Consequences
3.9 Fixed Points via Two Metrics
Part II Fixed Point Theorems on Various Metric Spaces
4 Generalization of Metric Spaces
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4.1 bb-Metric Space
4.2 Partial Metric Spaces
4.3 On Further Extension of the Metric Notion: Overview
5 Fixed Point Theorems on bb-Metric Spaces
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5.1 Fixed Point Theorems via Admissible Mappings
5.2 Nonunique Fixed Points Theorems
6 Fixed Point Theorems in Partial Metric Spaces
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6.1 Fixed Point Theorems via Admissible Mappings
6.2 Nonunique Fixed Points Theorems
References
Index
