Functional Equations and Inequalities with Applications

The field of functional equations is an ever-growing branch of mathematics with far-reaching applications. This book presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations and their applications to related topics.

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.

This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.

The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition.

Offers a comprehensive coverage of most relevant and classic functional equations Provides a in-depth introductory chapter to support the various topics discussed in later chapters Basic reference work for functional equations and inequalities Emphasis on real-world applications in a variety of other disciplines such as topology, economics, business management, physics, geometry, statistics, and behavioral sciences A link is established between the fundamental families of equations and the various approaches and methods that are used to implement them

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Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.

This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.

The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition.

Contenu
Basic Equations: Cauchy and Pexider Equations.- Matrix Equations.- Trigonometric Functional Equations.- Quadratic Functional Equations.- Characterization of Inner Product Spaces.- Stability.- Characterization of Polynomials.- Nondifferentiable Functions.- Characterization of Groups, Loops, and Closure Conditions.- Functional Equations from Information Theory.- Abel Equations and Generalizations.- Regularity ConditionsChristensen Measurability.- Difference Equations.- Characterization of Special Functions.- Miscellaneous Equations.- General Inequalities.- Applications.