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