A Generalized Nonlinear Random Equations with Random Fuzzy Mappings in Uniformly Smooth Banach Spaces

Nawitcha Onjai-Uea,Poom Kumam

doi:10.1155/2010/728452

Abstract

We introduce and study the general nonlinear random -accretive equations with random fuzzy mappings. By using the resolvent technique for the -accretive operators, we prove the existence theorems and convergence theorems of the generalized random iterative algorithm for this nonlinear random equations with random fuzzy mappings in -uniformly smooth Banach spaces. Our result in this paper improves and generalizes some known corresponding results in the literature.

Highlights

Fuzzy Set Theory was formalised by Professor Lofti Zadeh at the University of California in 1965 with a view to reconcile mathematical modeling and human knowledge in the engineering sciences
In 1997, Huang 3 first introduced the concept of random fuzzy mapping and studied the random nonlinear quasicomplementarity problem for random fuzzy mappings
Inspired and motivated by recent works in these fields see 2, 13, 14, 18–29, in this paper, we introduce and study a class of general nonlinear random equations with random fuzzy mappings in Banach spaces

Summary

Introduction

Fuzzy Set Theory was formalised by Professor Lofti Zadeh at the University of California in 1965 with a view to reconcile mathematical modeling and human knowledge in the engineering sciences. Huang studied the random generalized nonlinear variational inclusions for random fuzzy mappings in Hilbert spaces. Journal of Inequalities and Applications studied a class of random generalized nonlinear mixed variational inclusions for random fuzzy mappings and constructed an iterative algorithm for solving such random problems. Lan et al 11 , introduced and studied a class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces and an iterative algorithm with errors for this nonlinear random multivalued operator equations. Inspired and motivated by recent works in these fields see 2, 13, 14, 18–29 , in this paper, we introduce and study a class of general nonlinear random equations with random fuzzy mappings in Banach spaces. Our results improve and extend the corresponding results of recent works

Preliminaries

Random Iterative Algorithms

Existence and Convergence Theorems