Iterative Functional Equations

ISBN-13: 9780521355612 / Angielski / Twarda / 1990 / 576 str.

M. Kuczma; R. Ger; B. Choczewski

Opis

A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.

Recenzje

"...a cohesive and exhaustive account of contemporary theory of iterative functional equations. It contains many results that have appeared before only in the research literature....the most representative publication on iterative functional equations in the literature." Jaroslav Smítal, Mathematical Reviews

Spis treści

Preface; Symbols and conventions; 1. Introduction; 2. Iteration; 3. Linear equations and branching processes; 4. Regularity of solutions of linear equations; 5. Analytic and integrable solutions of linear equations; 6. Theory of nonlinear equations; 7. Equations of higher orders and systems of linear equations; 8. Equations of infinite order and systems of nonlinear equations; 9. On conjugacy; 10. More on the Schröder and Abel equations; 11. Characterization of functions; 12. Iterative roots and invariant curves; 13. Linear iterative functional inequalities; References; Author index; Subject index.