Multiplicative Inverse Functional Equations: Theory and Applications: 289 (Studies in Systems, Decision and Control, 289)

✍ Scribed by B. V. Senthil Kumar, Hemen Dutta

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 124
• Edition: 1st ed. 2020
• Category: Library

✦ Synopsis

This book introduces readers to numerous multiplicative inverse functional equations and their stability results in various spaces. This type of functional equation can be of use in solving many physical problems and also has significant relevance in various scientific fields of research and study. In particular, multiplicative inverse functional equations have applications in electric circuit theory, physics, and relations connecting the harmonic mean and arithmetic mean of several values. Providing a wealth of essential insights and new concepts in the field of functional equations, the book is chiefly intended for researchers, graduate schools, graduate students, and educators, and can also used for seminars in analysis covering topics of functional equations. 

✦ Table of Contents

Preface
Contents
About the Authors
1 Introduction to Functional Equations and Ulam Stability Theory
1.1 Significance of Functional Equations
1.2 Application of Functional Equation in Geometry
1.3 Application of Functional Equation in Financial Management
1.4 Application of Functional Equation in Information Theory
1.5 Application of Functional Equation in Wireless Sensor Networks
1.6 Interpretation of Multiplicative Inverse Functional Equations
1.6.1 Geometrical Interpretation of Eq. (1.17)
1.6.2 An Application of Eq. (1.17) to Resistances connected in parallel
1.7 Relevance of RQD and RQA Functional Equations
1.8 Ulam's Motivation Problem for Stability of Functional Equation
1.9 Stability of Functional Equation Incorporated with a Positive Constant (or H-U Stability)
1.10 Stability of Functional Equation Incorporated with Sum of Exponents of Norms (or H-U-R Stability)
1.11 Stability of Functional Equation Incorporated with Product of Exponents of Norms (or U-G-R Stability)
1.12 Stability of Functional Equation Involving a General Control Function (or Generalized H-U-R Stability)
1.13 Stability Involving Assorted Type of Multiplication-Addition of Exponents of Norms (or JMR Stability)
1.14 Various Types of Functional Equations
2 Stability and Instability of Multiplicative Inverse Type Tredecic and Quottuordecic Functional Equations in Non-archimedean Spaces
2.1 Introduction
2.2 Preliminaries
2.3 Fundamental Stabilities of Eqs. (2.1) and (2.2)
2.4 Counter-Examples
3 Estimation of Inexact Multiplicative Inverse Type Quindecic and Sexdecic Functional Equations in Felbin's Type Fuzzy Normed Spaces
3.1 Introduction
3.2 Preliminaries
3.3 Fuzzy Stabilities of Eqs.(3.1) and (3.2) via Fixed Point Method
3.4 Counter-Examples
4 Classical Approximations of Multiplicative Inverse Type Septendecic and Octadecic Functional Equations in Quasi-β-normed Spaces
4.1 Introduction and Preliminaries
4.2 Fundamental Stabilities of Eqs. (4.1) and (4.2)
4.3 Counter-Examples
5 Ulam Stabilities of Multiplicative Inverse Type Novemdecic and Vigintic Functional Equations in Intuitionistic Fuzzy Normed Spaces
5.1 Introduction
5.2 Preliminaries
5.3 Ulam Stabilities of Eqs. (5.1) and (5.2)
5.4 Counter-Examples
6 Solution to the Ulam Stability Problem of Multiplicative Inverse Type Unvigintic and Duovigintic Functional Equations in Paranormed Spaces
6.1 Introduction
6.2 Preliminaries
6.3 Stability of (6.1): Direct Method
6.4 Stability of (6.2): Direct Method
6.5 Stability of (6.1): Fixed Point Method
6.6 Stability of (6.2): Fixed Point Method
6.7 Counter-Examples
7 Inexact Solution of Multiplicative Inverse Type Trevigintic and Quottuorvigintic Functional Equations in Matrix Normed Spaces
7.1 Introduction
7.2 Stability of Eq. (7.1) in matrix normed spaces
7.3 Stability of Eq. (7.2) in matrix normed spaces
7.4 Counter-Examples
Appendix References