Topics in Contemporary Mathematical Analysis and Applications

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Editor
Contributors
Chapter 1 Certain Banach-Space Operators Acting on Free Poisson Elements Induced by Orthogonal Projections
1.1 Introduction
1.2 Preliminaries
1.3 Some Banach *-Algebras Induced by Projections
1.4 Weighted-Semicircular Elements Induced by Q
1.5 Semicircular Elements Induced by Q
1.6 The Semicircular Filterization (L[sub(Q)], Ί)
1.7 Free Poisson Elements of L[sub(Q)]
1.7.1 Free Poisson Elements
1.7.2 Certain Free Poisson Elements Induced by S
1.7.3 Some Free Poisson Elements Induced by S U X
1.8 Free Weighted-Poisson Elements of L[sub(Q)]
1.8.1 Free Weighted-Poisson Elements
1.8.2 Free Weighted-Poisson Elements Induced by S U X
1.8.3 Free Weighted-Poisson Elements Induced by X
1.9 Shifts on Z and Integer-Shifts on L[sub(Q)]
1.9.1 (±)-Shifts on Z
1.9.2 Integer-Shifts on L[sub(Q)]
1.9.3 Free Probability on L[sub(Q)] Under the Group-Action of B
1.10 Banach-Space Operators on L[sub(Q)] Generated by B
1.10.1 Deformed Free Probability of L[sub(Q)] by A
1.10.2 Deformed Semicircular Laws on L[sub(Q)] by A
1.11 Deformed Free Poisson Distributions on L[sub(Q)] by A
References
Chapter 2 Linear Positive Operators Involving Orthogonal Polynomials
2.1 Operators Based on Orthogonal Polynomials
2.1.1 Notations
2.1.2 Definitions
2.1.3 Appell Polynomials
2.1.4 Boas-Buck-Type Polynomials
2.1.5 Charlier Polynomials
2.1.6 Approximation by Appell Polynomials
2.1.7 Approximation by Operators Including Generalized Appell Polynomials
2.1.8 Szász-Type Operators Involving Multiple Appell Polynomials
2.1.9 Kantorovich-Type Generalization of K[sub(n)] Operators
2.1.10 Kantorovich Variant of Szász Operators Based on Brenke-Type Polynomials
2.1.11 Operators Defined by Means of Boas-Buck-Type Polynomials
2.1.12 Operators Defined by Means of Charlier Polynomials
2.1.13 Operators Defined by Using q-Calculus
Acknowledgment
References
Chapter 3 Approximation by Kantorovich variant of l??Schurer Operators and Related Numerical Results
3.1 Introduction
3.2 Auxiliary Results
3.3 Approximation Behavior of λ-Schurer-Kantorovich Operators
3.4 Voronovskaja-type Approximation Theorems
3.5 Graphical and Numerical Results
3.6 Conclusion
References
Chapter 4 Characterizations of Rough Fractional-Type Integral Operators on Variable Exponent Vanishing Morrey-Type Spaces
4.1 Introduction
4.2 Preliminaries and Main Results
4.2.1 Variable Exponent Lebesgue Spaces L[sup(P(·))]
4.2.2 Variable Exponent Morrey Spaces L[sup(P(·))],λ[sup(·)]
4.2.3 Variable Exponent Vanishing Generalized Morrey Spaces
4.2.4 Variable Exponent-Generalized Campanato Spaces C[sub(Π)][sup(q(·),ɣ(·))]
4.3 Conclusion
Funding
References
Chapter 5 Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices
5.1 Introduction
5.2 Preliminaries
5.3 pτ-Continuous and pτ-Bounded Operators
5.4 upτ-Continuous Operators
5.5 The Compact-Like Operators
Bibliography
Chapter 6 On Indexed Product Summability of an Infinite Series
6.1 Introduction
6.1.1 Historical Background
6.1.2 Notations and Definitions
6.2 Known Results
6.3 Main Results
6.4 Proof of Main Results
6.5 Conclusion
References
Chapter 7 On Some Important Inequalities
7.1 Concepts of Affinity and Convexity
7.1.1 Affine and Convex Sets and Functions
7.1.2 Effect of Affine and Convex Combinations in R[sup(n)]
7.1.3 Coefficients of Affine and Convex Combinations
7.1.4 Support and Secant Hyperplanes
7.2 The Jensen Inequality
7.2.1 Discrete and Integral Forms of the Jensen Inequality
7.2.2 Generalizations of the Jensen Inequality
7.3 The Hermite-Hadamard Inequality
7.3.1 The Classic Form of the Hermite-Hadamard Inequality
7.3.2 Generalizations of the Hermite-Hadamard Inequality
7.4 The Rogers-Hölder Inequality
7.4.1 Integral and Discrete Forms of the Rogers-Hölder Inequality
7.4.2 Generalizations of the Rogers-Hölder Inequality
7.5 The Minkowski Inequality
7.5.1 Integral and Discrete Forms of the Minkowski Inequality
7.5.2 Generalizations of the Minkowski Inequality
Bibliography
Chapter 8 Refinements of Young’s Integral Inequality via Fundamental Inequalities and Mean Value Theorems for Derivatives
8.1 Young’s Integral Inequality and Several Refinements
8.1.1 Young’s Integral Inequality
8.1.2 Refinements of Young’s Integral Inequality via Lagrange’s Mean Value Theorem
8.1.3 Refinements of Young’s Integral Inequality via Hermite-Hadamard’s and Čebyšev’s Integral Inequalities
8.1.4 Refinements of Young’s Integral Inequality via Jensen’s Discrete and Integral Inequalities
8.1.5 Refinements of Young’s Integral Inequality via H¨older’s Integral Inequality
8.1.6 Refinements of Young’s Integral Inequality via Taylor’s Mean Value Theorem of Lagrange’s Type Remainder
8.1.7 Refinements of Young’s Integral Inequality via Taylor’s Mean Value Theorem of Cauchy’s Type Remainder and H¨older’s Integral Inequality
8.1.8 Refinements of Young’s Integral Inequality via Taylor’s Mean Value Theorem of Cauchy’s Type Remainder and Čebyšev’s Integral Inequality
8.1.9 Refinements of Young’s Integral Inequality via Taylor’s Mean Value Theorem of Cauchy’s Type Remainder and Jensen’s Inequalities
8.1.10 Refinements of Young’s Integral Inequality via Taylor’s Mean Value Theorem of Cauchy’s Type Remainder and Integral Inequalities of Hermite-Hadamard Type for the Product of Two Convex Functions
8.1.11 Three Examples Showing Refinements of Young’s Integral Inequality
8.1.11.1 First Example
8.1.11.2 Second Example
8.1.11.3 Third Example
8.2 New Refinements of Young’s Integral Inequality via Pólya’s Type Integral Inequalities
8.2.1 Refinements of Young’s Integral Inequality in Terms of Bounds of the First Derivative
8.2.2 Refinements of Young’s Integral Inequality in Terms of Bounds of the Second Derivative
8.2.3 Refinements of Young’s Integral Inequality in Terms of Bounds of Higher-Order Derivatives
8.2.4 Refinements of Young’s Integral Inequality in Terms of L[sup(p)]-Norms
8.2.5 Three Examples for New Refinements of Young’s Integral Inequalities
8.2.5.1 First Example
8.2.5.2 Second Example
8.2.5.3 Third Example
8.3 More Remarks
Acknowledgments
Bibliography
Chapter 9 On the Coefficient Estimates for New Subclasses of Biunivalent Functions Associated with Subordination and Fibonacci Numbers
9.1 The Definition and Elementary Properties of Univalent Functions
9.1.1 Integral Operators
9.2 Subclasses of Analytic and Univalent Functions
9.3 The Class Σ
9.4 Functions with Positive Real Part
9.4.1 Subordination
9.5 Bi-univalent Function Classes S[sub(t,Σ)][sup(μ)] and K[sub(t,Σ)][sup(μ)] (P̃)
9.6 Inequalities for the Taylor-Maclaurin Coefficients
9.7 Concluding Remarks and Observations
Acknowledgment
Bibliography
Chapter 10 Fixed Point of Multivalued Cyclic Contractions
10.1 Multivalued Mappings in Metric Spaces
10.2 Multivalued Cyclic F-Contractive Mappings
10.3 Fixed Point Results of Multivalued Cyclic F-Contractive Mappings
10.4 Stability of Fixed Point Sets of Cyclic F-Contractions
10.5 Multivalued Mappings under Cyclic Simulation Function
10.6 Fixed Point Theorems under Cyclic Simulation Function
10.7 Stability of Fixed Point Sets under Cyclic Simulation Function
Bibliography
Chapter 11 Significance and Relevances of Functional Equations in Various Fields
11.1 Introduction
11.2 Application of Functional Equation in Geometry
11.3 Application of Functional Equation in Financial Management
11.4 Application of Functional Equation in Information Theory
11.5 Application of Functional Equation in Wireless Sensor Networks
11.6 Application of Rational Functional Equation
11.6.1 Geometrical Interpretation of Equation (11.17)
11.6.2 An Application of Equation (11.17) to Resistances Connected in Parallel
11.7 Application of RQD and RQA Functional Equations
11.8 Application of Other Multiplicative Inverse Functional Equations
11.8.1 Multiplicative Inverse Second Power Difference and Adjoint Functional Equations
11.8.2 Multiplicative Inverse Third Power Functional Equation
11.8.3 Multiplicative Inverse Fourth Power Functional Equation
11.8.4 Multiplicative Inverse Quintic Functional Equation
11.8.5 Multiplicative Inverse Functional Equation Involving Two Variables
11.8.6 System of Multiplicative Inverse Functional Equations with Three Variables
11.9 Applications of Functional Equations in Other Fields
11.10 Open Problems
Bibliography
Chapter 12 Unified-Type Nondifferentiable Second-Order Symmetric Duality Results over Arbitrary Cones
12.1 Introduction
12.2 Literature Review
12.3 Preliminaries and Definitions
12.3.1 Definition
12.3.2 Definition
12.3.3 Definition
12.3.4 Definition
12.4 Nondifferentiable Second-Order Mixed-Type Symmetric Duality Model Over Arbitrary Cones
12.4.1 Remarks
12.5 Duality Theorems
12.6 Self-Duality
12.7 Conclusion
Bibliography
Index