Nonlinear operator theory in probabilistic metric spaces. (English) Zbl 1080.47054

Huntington, NY: Nova Science Publishers (ISBN 1-56072-980-5/hbk). 338 p. ; (2001).
Publisher’s description: The purpose of this book is to give a comprehensive introduction to the study of nonlinear operator theory in probabilistic metric spaces. It gives a survey of the latest and new results on the following topics: 1. Basic theory of probabilistic metric spaces, 2. Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces, 3. Ekeland’s variational principle and Caristi’s fixed point theorem in probabilistic metric spaces, 4. Coincidence point theorems, minimization and fixed degree theorems in probabilistic metric spaces, 5. Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces, 6. Nonlinear semigroups and differential equations in probabilistic metric spaces, 7. KKM theorems, minimax theorems and variational inequalities.


47S50 Operator theory in probabilistic metric linear spaces
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47Hxx Nonlinear operators and their properties
47Jxx Equations and inequalities involving nonlinear operators