Fixed Point Theory in Probabilistic Metric Spaces / Edition 1

by O. Hadzic, E. Pap

Overview

Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory.
Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces.
In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces.
Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.

Product Details

ISBN-13:	9781402001291
Publisher:	Springer Netherlands
Publication date:	11/30/2001
Series:	Mathematics and Its Applications , #536
Edition description:	2001
Pages:	273
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Introduction. 1. Triangular norms. 2. Probabilistic metric spaces. 3. Probabilistic £Ii£-contraction principles for single-valued mappings. 4. Probabilistic £Ii£-contraction principles for multi-valued mappings. 5. Hicks' contraction principle. 6. Fixed point theorems in topological vector spaces and applications to random normed spaces. Bibliography. Index.

Editorial Reviews

The aim Hadzi'c and Pap (both of the Institute of Mathematics, U. of Novi Sad, Yugoslavia) is to stimulate interest among scientists and students in fixed point theory, which can be considered a part of probabilistic analysis. After an overview of basic definitions and examples from the fixed point theory and a discussion of the closely related theory of triangular norms, the bulk of the book deals with some single-valued and multi-valued probabilistic versions of the Banach contraction formula. Finally, a chapter is devoted to fixed point theorems in topological vector spaces and applications to random spaced norms. Annotation c. Book News, Inc., Portland, OR (booknews.com)