Advanced Mathematical Analysis and its Applications

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Editor Biographies
List of Contributors
Chapter 1 Generalized Boyd-Wong-Type Contractions and Related Fixed-FigureResults
1.1 Introduction and Preliminaries
1.2 Generalized Boyd-Wong-Type Fixed-Figure Results
1.3 Conclusion and FutureWork
Bibliography
Chapter 2 Remarks on the Metatheorem in Ordered Fixed PointTheory
2.1 Introduction
2.2 The 2023 Metatheorem
2.3 The 2022 Metatheorem
2.4 Examples of Metatheorem
2.4.1 Brézis-Browder in 1976
2.4.2 Fierro in 2015
2.4.3 Fierro in 2017
2.4.4 Fierro in 2021
2.5 Comments on Works of Other Authors
2.5.1 Fierro
2.5.2 Boros, Iqbal, and Száz
2.5.3 Boros, Iqbal, and Száz
2.5.4 Iqbal and Száz
2.6 Our Resolution and New Caristi Theorem
2.7 Epilogue
Bibliography
Chapter 3 On Wardowski Type Results in the Framework of G-Metric Spaces
3.1 Introduction and Preliminaries
3.2 Main Results
3.3 Conclusion
Bibliography
Chapter 4 Some New Fixed Point Results in Archimedean Type Intuitionistic Fuzzy b-Metric Space
4.1 Introduction
4.2 Some Basic Definitions
4.3 Some Fixed Point Theorems and Related Propositions
4.3.1 Definitions
4.3.2 Theorems
4.4 Application
4.5 Conclusion
Bibliography
Chapter 5 Fixed Point Theorems for Quasi Upper Semicontinuous Set-valued Mappings in p-Vector and Locally p-Convex Spaces
5.1 Introduction
5.2 Some Basic Notions and Results of p-Vector Spaces
5.3 Fixed Point Theoremsin p-Vector Spaces and Locally p-Convex Spaces
Acknowledgment
Compliance with Ethical Standards
Bibliography
Chapter 6 Proinov Es-Contraction Type Unique and Non-Unique Fixed-Point Results on S-Metric Spaces
6.1 Introduction and Motivation
6.2 Main Results
6.2.1 Some Fixed-Point Results
6.2.2 Some Fixed-Figure Results
6.2.2.1 Some Fixed-Disc Results
6.2.2.2 Some Fixed-Ellipse Results
6.2.2.3 Some Fixed-Hyperbola Results
6.2.2.4 Some Fixed-Cassini Curve Results
6.2.2.5 Some Fixed-Apollonius Circle Results
Bibliography
Chapter 7 A-Admissible Mappings for Four Maps in C*-Algebra-Valued MP-Metric Spaces with an Application
7.1 Introduction
7.2 ηA-Admissible Mapping in C* -Contraction
7.3 ηA-Admissible Mapping in Kannan-Ćirić C*-Contraction
7.4 Example
7.5 Application
7.6 Conclusion
Bibliography
Chapter 8 Summarized Proofs to Find Common Fixed Points of Prešic Contractions for Four Maps
8.1 Introduction
8.2 Main Results
8.3 Example
8.4 Prešić-Hardy-Rogers Type Fixed Point Results
8.5 Example
8.6 Application
8.7 Conclusion
Bibliography
Chapter 9 Fixed Point Method: Ulam Stability of Mixed Type Functional Equation in ß-Banach Modules
9.1 Introduction
9.2 Main Results
9.2.1 Stability Results: When f Is Odd
9.2.2 Stability Results: When f Is Even
9.2.3 Stability Results for the Mixed Case
9.3 Conclusion
Bibliography
Chapter 10 Hybrid Steepest Descent Methods for SolvingVariational Inequalities with Fixed Point Constraints in a Hilbert Space: An Annotated Bibliography
10.1 Introduction
10.1.1 Hybrid Steepest Descent Method (HSDM)
10.1.2 Scope of the Paper and an Apology
10.1.3 Organization of the Paper
10.2 Some Works of Fixed Point Constraints before HSDM
10.3 The Development of HSDM
10.3.1 VIP (F, FixT)
10.3.2 VIP (F, [sup(m)]∩[sub(i=1)] FixT[sub(i)])
10.4 Conclusions
Bibliography
Chapter 11 Generalized Kannan Maps with Application to Iterated Function System
Abbreviations and Notations
Abbreviations
Notations
11.1 Introduction
11.2 Generalized Kannan Map
11.3 Application to Iterated Function System
11.4 Conclusion
Bibliography
Chapter 12 Stability Analysis of Lotka-Volterra Models: Continuous, Discrete and Fractional
12.1 Introduction
12.2 The Modified Lotka–Volterra Model
12.2.1 Model Description
12.2.2 Non-Negativity and Boundedness of the Solutions
12.2.3 Stability Analysis
12.2.4 Graphical Analysis
12.3 Euler’s Numerical Scheme
12.3.1 Model Discretization
12.3.2 Non-Negativity and Boundedness of the Solutions
12.3.3 Stability Analysis
12.3.4 Graphical Analysis
12.4 Mickens’ Numerical Scheme
12.4.1 Model Discretization
12.4.2 Non-Negativity and Boundedness of Solutions
12.4.3 Stability Analysis
12.4.4 Graphical Analysis
12.5 Fractional Calculus (FC)
12.5.1 Preliminaries on FC
12.5.2 Model Description
12.5.3 Existence and Uniqueness
12.5.4 The Boundedness Condition
12.5.5 Stability Analysis
12.5.6 Graphical Analysis
12.6 Conclusions
Acknowledgments
Bibliography
Chapter 13 Existence and Uniqueness of Solutions to Proper Fractional Riemann-Liouville Initial Value Problems on Time Scales
13.1 Introduction
13.2 Preliminaries
13.3 Main Results
13.3.1 Properties of theTime-Scale Fractional Operators
13.3.2 Existence of Solutions to Fractional IVPs on Time Scales
13.4 Acknowledgments
Bibliography
Chapter 14 Ostrowski Type Inequalities for Conformable Fractional Calculus via a Parameter
14.1 Introduction
14.2 Preliminary Notes
14.3 The Conformable Ostrowski’s Integral Inequality with a Parameter
14.4 Other Bounds for the Conformable Fractional Ostrowski Type Inequalities via a Parameter
14.5 Conclusion
Bibliography
Chapter 15 The Regional Observability Problem for a Class of Semilinear Time-Fractional Systems With Riemann-Liouville Derivative
15.1 Introduction
15.2 An Overview of the Considered System
15.3 The Reconstruction Approach
Algorithm
15.4 Example
15.5 Conclusion
Bibliography
Chapter 16 Construction of Fractional Extended Nabla Operator and Strong Convergence Analysis
16.1 Introduction
16.2 Preliminaries on Operators in Hölder Spaces
16.3 Fractional Power of Sectorial Operator
16.3.1 Sectorial Property
16.3.2 Fractional Power of the Derivative
16.3.3 Fractional Nabla Operators
16.4 Hölderian Convergence of Fractional Extended Nabla Operator to Fractional Derivative
16.5 Numerical Examples
Example16.1
Example16.2
16.6 Conclusion
Note
Bibliography
Chapter 17 Stability Analysis of Fractional Nonlinear Dynamical Systems
17.1 Introduction
17.1.1 Birth of Fractional Calculus
17.1.2 Motivation
17.2 Preliminaries
17.2.1 Laplace Transform
17.3 Stability Analysis of Some Special Nonlinear Fractional Differential Systems
17.3.1 Stability of Fractional Nonlinear System
17.3.2 Stability of Fractional Neutral Differential Equations
17.3.3 Stability of Fractional Langevin Differential Equations
17.3.4 Stability of a Fractional Delay Differential System
17.4 Numerical Examples
17.5 Conclusion
Bibliography
Chapter 18 On Periodic Dirichlet Series and Special Functions
18.1 Introduction
18.1.1 Notation and Terminology
18.2 Dirichlet Series with Periodic Coefficients
18.3 Parityand Restatement of the Main Theorem
18.4 Algebraic Elucidation of Analytic Expressions
Acknowledgment
Bibliography
Chapter 19 The Lotka-Volterra Dynamical Systemand Its Discretization
19.1 Introduction to the Lotka–Volterra Model
19.2 Discretization by Euler’s Method
19.3 Discretization by Mickens’ Method
19.4 Conclusion
Acknowledgments
Bibliography
Chapter 20 A New Inertial Projection Algorithm for Solving Pseudomonotone Equilibrium Problems
20.1 Introduction
20.2 Preliminaries
20.3 The Algorithm and Convergence Analysis
20.4 Rate of Convergence
20.5 Computational Experiments
20.5.1 Test 1
20.5.2 Test 2
20.6 Conclusion
Bibliography
Chapter 21 Convergence Analysis of a Relaxed Inertial Alternating Minimization Algorithm with Applications
21.1 Introduction
21.2 Preliminaries
21.3 Relaxed Inertial Three-Block AMA for Solving Three-Block Separable Convex Minimization Problem
21.4 Numerical Experiments
21.4.1 Stable Principal Component Pursuit
21.4.2 Parameters Setting
21.4.3 Results and Discussion
21.5 Conclusions
Bibliography
Chapter 22 Ball Convergence of Iterative Methods without Derivatives with or without Memory Relying on the Weight Operator Technique
22.1 Introduction
22.2 Ball Convergence
22.3 Numerical Examples
22.4 Conclusion
Bibliography
Chapter 23 Inner Product Generalized Trapezoid Type Inequalities in Hilbert Spaces
23.1 Introduction
23.2 Main Results
23.3 Inequalities for Operator Monotone Functions
23.4 Some Examples
Bibliography
Chapter 24 A Note on Degenerate Gamma Random Variables
24.1 Introduction
24.2 Degenerate Gamma Random Variables
24.3 Further Remark
Bibliography
Chapter 25 Dynamical Systems on Free Random Variables Followed by the Semicircular Law
25.1 Introduction
25.1.1 Motivations
25.1.2 Overview
25.2 Preliminaries
25.3 On |N|-Many Semicircular Elements
25.3.1 A C*-Algebra X Generated by X
25.3.2 Certain Free-Isomorphisms on X[sub(φ)]
25.4 Free Random Variables Followed by the Semicircular Law
25.4.1 The C*-Algebra Λ Generated by the Integer-Shift Group λ
25.4.2 On the Tensor Product Λ  X
25.5 A Group-Dynamical System (Z, X[sub(τ)], α)
25.5.1 Dynamicson (Z, X[sub(τ)], α)
25.5.2 The Crossed Product C*-Algebra X[Γ] of Γ
25.5.3 Free-Distributional Data on X[Γ]
25.5.4 Discussion: Z-Dynamics on X[sub(τ)]
25.6 More About Free-Distributional Data on X[Γ]
25.6.1 Free Random Variables of X [Γ] Followed by the Circular Law
25.6.1.1 Free Random Variables Followed by The Circular Law
25.6.2 Free Random Variables of X [Γ] Followed by Free Poisson Distributions
Bibliography
Index