This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.
Author(s): Pradip Debnath, Nabanita Konwar, Stojan Radenović
Series: Forum for Interdisciplinary Mathematics
Publisher: Springer
Year: 2022
Language: English
Pages: 362
City: Singapore
Preface
Contents
About the Editors
Basic Fixed Point Theorems in Metric Spaces
1 Introduction
2 Banach's Contraction Mapping Principle
3 Generalizations of Contraction Mapping Principle
4 Metric Fixed Point Without Continuity
5 Remark
References
Study of Fixed Point Theorem and Infinite Systems of Integral Equations
1 Introduction
1.1 Axiomatic Approach to the Concept of an MNC
1.2 Hausdorff Measure of Noncompactness (HMNC)
2 Fixed Point Theorems
3 Application of Fixed Point on Integral Equations
3.1 Solvability of Infinite System of Functional Integral Equations in c0
3.2 Solvability of Infinite System of Functional Integral Equations in ell1
References
Common Fixed Point Theorems and Applications in Intuitionistic Fuzzy Cone Metric Spaces
1 Introduction
2 Preliminaries
3 Some Common Fixed Point Theorems in IFCMS
References
Modular Spaces and Fixed Points of Generalized Contractions
1 Introduction
2 Main Results
References
Fixed-Point Theorems in Generalized Modular Metric Spaces
1 Metrics and Modulars
2 Fixed-Point Theorems in Generalized Modular Metric Spaces
2.1 The Banach Contraction Principle in Generalized Modular Metric Spaces
2.2 Ćirić Quasi-contraction in Generalized Modular Metric Spaces
2.3 Topology on Generalized Modular Metric Spaces
3 Feng-Liu Theorem in GMMS
3.1 Multivalued Mappings in GMMS
References
On Some Fixed Point Results in Various Types of Modular Metric Spaces
1 Introduction
2 Fixed Point Results in non-Archimedean Modular Metric Space
3 Fixed Point Results in Non-Archimedean Quasi Modular Metric Space
4 Conclusions
References
On Parametric (b, θ)-Metric Space and Some Fixed Point Theorems
1 Introduction
2 Preliminaries
3 Main Results
4 Application
References
Some Extragradient Methods for Solving Variational Inequalities Using Bregman Projection and Fixed Point Techniques in Reflexive Banach Spaces
1 Introduction
2 Preliminaries
3 Main Results
3.1 Convergence Analysis
3.2 Convergence Analysis
3.3 Convergence Analysis
4 Numerical Experiments
5 Conclusion
References
Common Solutions to Variational Inequality Problem via Parallel and Cyclic Hybrid Inertial CQ-Subgradient Extragradient Algorithms in (HSs)
1 Introduction
2 Crucial Lemmas
3 Main Theorems
4 Numerical Results
4.1 A Strong Convergence in mathbbR3
4.2 A Strong Convergence in L2
5 Conclusions
References
On a New Class of Interval-Valued Variational Control Problems
1 Introduction
2 Preliminaries
3 Interval-Valued KT-pseudoinvex Optimization Problems
4 An Interval-Valued Optimization Problem Associated with (OP) with Modified Objective Functional
5 Saddle-Point Optimality Criteria
6 Conclusions
References
Best Proximity Points for Multivalued Mappings Satisfying Zσ-Proximal Contractions with Applications
1 Introduction and Preliminaries
2 Multivalued Suzuki-Type Zσ-Contractions
3 Some Applications
4 Conclusion
References
Coincidence Best Proximity Point Results via wp-Distance with Applications
1 Introduction
2 Preliminaries
3 Weakly Kannan Type Best Proximity Points via wp-Distance
4 Results in Partially Ordered Metric Space
5 Application to Fixed-Point Theory
6 Conclusion
References
Application of Fixed Point Iterative Methods to Construct Fractals and Anti-fractals
1 Introduction
2 Preliminaries
3 Main Results
3.1 Escape Criterion for Quadratic Complex Polynomials
3.2 Escape Criterion for Cubic Complex Polynomials
3.3 Escape Criterion for General Complex Polynomials
4 Algorithm for Generating Fractals
5 Construction of Mandelbrot Sets in the Suantai Type Orbit
5.1 Mandelbrot Sets for Quadratic Polynomials
5.2 Mandelbrot Sets for Higher Degree Polynomials
6 Construction of Julia Sets in the Suantai Type Orbit
6.1 Julia Sets for Quadratic Complex Polynomials
6.2 Julia Sets for Higher Degree Polynomials
7 Generation of Anti-fractals in the Suantai Type Orbit
7.1 Construction of Tricorns and Multicorns
8 Construction of Anti-Julia Sets
9 Conclusion
References
Nonexpansive Mappings, Their Extensions, and Generalizations in Banach Spaces
1 Introduction
2 Preliminaries
3 Fixed Point Theorems for Nonexpansive Mappings
4 Some Extensions and Generalizations of Nonexpansive Mappings
5 Suzuki-Type Generalized Nonexpansive Mappings
6 Convergence of Fixed Points of Nonexpansive Type Mappings
References
A Mathematical Model Using Fixed Point Theorem for Two-Choice Behavior of Rhesus Monkeys in a Noncontingent Environment
1 Introduction
2 An Experiment with Rhesus Monkeys
3 Modeling of the Problem Using Banach's Fixed Point Theorem
4 Main Results
5 Some Consequences of the Main Result
6 Discussion and Interpretation of the Problem in Hand
7 Conclusion and Future Work
References
