Introduction to Functional Equations

ISBN-13: 9781439841112 / Angielski / Twarda / 2011 / 465 str.

Prasanna K. Sahoo;Palaniappan Kannappan

Opis

Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces. Functional equations covered include:

• Cauchy Functional Equations and Applications
• The Jensen Functional Equation
• Pexider's Functional Equation
• Quadratic Functional Equation
• D'Alembert Functional Equation
• Trigonometric Functional Equations
• Pompeiu Functional Equation
• Hosszu Functional Equation
• Davison Functional Equation
• Abel Functional Equation
• Mean Value Type Functional Equations
• Functional Equations for Distance Measures

The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations.

Recenzje

The book includes several interesting and fundamental techniques for solving functional equations in real or complex realms. There exist many useful exercises as well as well-organized concluding remarks in each chapter. … This book is written in a clear and readable style. It is useful for researchers and students working in functional equations and their stability.
—Mohammad Sal Moslehian, Mathematical Reviews, Issue 2012b

Spis treści

Additive Cauchy Functional Equation. Remaining Cauchy Functional Equations. Cauchy Equations in Several Variables. Extension of Additive Functions. Applications of Cauchy Functional Equations. More Applications of Functional Equations. The Jensen Functional Equation. Pexider’s Functional Equations. Quadratic Functional Equation. D’Alembert Functional Equation. Trigonometric Functional Equations. Pompeiu Functional Equation. Hosszu Functional Equation. Davison Functional Equation. Abel Functional Equation. Mean Value Type Functional Equations. Functional Equations for Distance Measures. Stability of Additive Cauchy Equation. Stability of Exponential Cauchy Equations. Stability of d’Alembert and Sine Equations. Stability of Quadratic Functional Equations. Stability of Davison’s Functional Equation.