Functional Equations and Inequalities

Solutions and Stability Results

This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.

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Contents:

• Functional Equations and Applications
• Historical Development of Functional Equations
• Methods of Solving Functional Equations
• General Solution of Euler–Lagrange Quadratic Type Functional Equations
• General Solution of Cubic Type Functional Equations
• General Solution of Quartic Type Functional Equations
• General Solution of Quintic and Sextic Functional Equations
• Mixed Type Functional Equations
• Mixed Type Functional Equations (continued)
• Two-Variable and Three-Variable Functional Equations
• The Ulam Stability Problem
• Stability of Functional Equations in Various Spaces
• Functional Inequalities
• Ulam–Hyers Stabilities of Functional Equations in Felbin's Normed Spaces
• Stabilities of Functional Equations on C*-algebras and Lie C*-algebras
• Ulam Stability of Mixed Type Mappings on Restricted Domains
• Related Topics on Distributions and Hyperfunctions and Jordan Lie Homomorphisms
• Exercises and Open Problems

Readership: Advanced undergraduates, postgraduates and researchers who are interested in functional equations and functional inequalities.
Key Features:

• The coverage in the volume is broad in nature and easily attracts anyone in search of this analytical topic
• This book begins with fundamental concepts, describes the growth of this field for the past four decades and it takes to the latest developments and findings that prevail in present research papers
• One of the authors, John Michael Rassias, is a well-known and world-leading mathematician in this field of functional equations