Topics in Contemporary Mathematical Analysis and Applications

Topics in Contemporary Mathematical Analysis and Applications

Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable ex...

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Detalles Bibliográficos
Otros Autores: Dutta, Hemen, 1981- editor (editor)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Boca Raton, FL : CRC Press 2021.
Edición:First edition
Colección:Mathematics and its applications : modelling, engineering, and social sciences.
Materias:
Mathematical analysis.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009645702606719
Tabla de Contenidos:
  • 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.

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