A new class of general nonlinear random set-valued variational inclusion problems involving A-maximal m-relaxed η-accretive mappings and random fuzzy mappings in Banach spaces

Narin Petrot,Javad Balooee

doi:10.1186/1029-242x-2012-98

Abstract

At the present article, we consider a new class of general nonlinear random A- maximal m-relaxed η-accretive equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By using the resolvent mapping technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang's lemma, we construct a new iterative algorithm with mixed errors for finding the approximate solutions of this class of nonlinear random equations. We also verify that the approximate solutions obtained by the our proposed algorithm converge to the exact solution of the general nonlinear random A-maximal m-relaxed η-accretive equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces.Mathematical Subject Classification 2010: Primary, 47B80; Secondary, 47H40, 60H25.

Highlights

The theory of variational inequalities was extended and generalized in many different directions because of its applications in mechanics, physics, optimization, economics and engineering sciences
We prove the existence of random solutions and the convergence of random iterative sequences generated by the our proposed algorithm in q-uniformly smooth Banach spaces
Let X be a q-uniformly smooth Banach space, A, p, η, M, N, S, T, P, Q, G, h, λ be the same as in the problem (3.1) and S, T, P, Q, G : Ω × X ® CB(X) be five random set-valued mappings induced by S, T, P, Q, G respectively

Summary

Introduction

The theory of variational inequalities was extended and generalized in many different directions because of its applications in mechanics, physics, optimization, economics and engineering sciences. Lan et al [53] introduced and studied a class of general nonlinear random set-valued operator equations involving generalized m-accretive mappings in Banach spaces.

Results

Conclusion