Iterative functional equations / Marek Kuczma, Bogdan Choczewski, Roman Ger.

Format:

Book

Author/Creator:

Kuczma, Marek, author.

Choczewski, Bogdan, author.

Ger, Roman, author.

Series:

Encyclopedia of mathematics and its applications ; v. 32.

Encyclopedia of mathematics and its applications ; volume 32

Language:

English

Subjects (All):

Functional equations.

Functions of real variables.

Physical Description:

1 online resource (xix, 552 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1990.

Language Note:

English

Summary:

A cohesive and exhaustive account of the modern theory of iterative functional equations.

Contents:

Cover; Half Title; Title; Copyright; PREFACE; SYMBOLS AND CONVENTIONS; 0 Introduction; 0.0 Preliminaries; 0.0A. Types of equations considered; 0.0B. Problems of uniqueness; 0.0C. Fixed points; 0.0D. General solution; 0.0E. Solution depending on an arbitrary function; 0.1 Special equations; 0.1A. Change of variables; 0.1B. Schröder's, Abel's and Böttcher's equations; 0.2 Applications; 0.2A. Synthesizing judgements; 0.2B. Clock-graduation and the concept of chronon; 0.2C. Sensation scale and Fechner's law; 0.3 Iterative functional equations; 1 Iteration; 1.0 Introduction

1.1 Basic notions and some substantial facts1.1A. Iterates, orbits and fixed points; 1.1B. Limit points of the sequence of iterates; 1.1C. Theorem of SarkovskiI; 1.1D. Attractive fixed points; 1.2 Maximal domains of attraction; 1.2A. Convergence of splinters; 1.2B. Analytic mappings; 1.3 The speed of convergence of iteration sequences; 1.3A. Some lemmas; 1.3B. Splinters behaving like geometric sequences; 1.3C. Slower convergence of splinters; 1.3D. Special cases; 1.4 Iteration sequences of random-valued functions; 1.4A. Preliminaries; 1.4B. Convergence of random splinters

1.5 Some fixed-point theorems1.5A. Generalizations of the Banach contraction principle; 1.5B. Case of product spaces; 1.5C. Equivalence statement; 1.6 Continuous dependence; 1.7 Notes; 2 Linear equations and branching processes; 2.0 Introduction; 2.1 Galton-Watson processes; 2.1A. Probability generating functions; 2.1B. Limit distributions; 2.1C. Stationary measures for processes with immigration; 2.1D. Restricted stationary measures for simple processes; 2.2 Nonnegative solutions; 2.2A. Negative g; 2.2B. Positive g; 2.3 Monotonic solutions; 2.3A. Homogeneous equation

2.3B. Special inhomogeneous equation2.3C. General inhomogeneous equation; 2.3D. An example; 2.3E. Homogeneous difference equation; 2.3F. Schröder's equation; 2.4 Convex solutions; 2.4A. Lemmas; 2.4B. Existence-and-uniqueness result; 2.4C. A difference equation; 2.4D. Abel's and Schröder's equations; 2.5 Regularly varying solutions; 2.5A. Regularly varying functions; 2.5B. Homogeneous equation; 2.5C. Special inhomogeneous equation; 2.6 Application to branching processes; 2.6A. Conditional limit probabilities; 2.6B. Stationary measures; 2.6C. Restricted stationary measures

2.7 Convex solutions of higher order2.7A. Definitions and results; 2.7B. A characterization of polynomials; 2.8 Notes; 3 Regularity of solutions of linear equations; 3.0 Introduction; 3.1 Continuous solutions; 3.1A. Homogeneous equation; 3.1B. General continuous solution of the homogeneous equation; 3.1C. Inhomogeneous equation; 3.2 Continuous dependence of continuous solutions on given functions; 3.3 Asymptotic properties of solutions; 3.3A. Solutions continuous at the origin; 3.3B. Sample proofs; 3.3C. Asymptotic series expansions; 3.3D. Solutions discontinuous at the origin

3.4 Differentiable solutions

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 504-545) and indexes.

ISBN:

1-139-88183-3

1-107-10264-2

1-107-08799-6

1-107-10010-0

1-107-09417-8

1-139-08663-4