A New System of Random Generalized Variational Inclusions with Random Fuzzy Mappings and Random --Accretive Mappings in Banach Spaces

Sayyedeh Zahra Nazemi

doi:10.5402/2012/731058

Abstract

We introduce a new notion of random --accretive mappings and prove the Lipschitz continuity of the random resolvent operator associated with the random --accretive mappings. We introduce and study a new system of random generalized variational inclusions with random --accretive mappings and random fuzzy mappings in Banach spaces. By using the random resolvent operator, an iterative algorithm for solving such system of random generalized variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of the iterative sequences generated by the algorithm.

Highlights

Variational inclusions and variational inequalities have wide applications to many fields including, for example, economics, optimization and control theory, operators research, transportation network modeling, and mathematical programming
We introduce a new notion of random H ·, ·, φ -η-accretive mappings and prove the Lipschitz continuity of the random resolvent operator associated with the random H ·, ·, φ -η-accretive mappings
We introduce and study a new system of random generalized variational inclusions with random H ·, ·, φ -η-accretive mappings and random fuzzy mappings in Banach spaces

Summary

Sayyedeh Zahra Nazemi

We introduce a new notion of random H ·, · , φ -η-accretive mappings and prove the Lipschitz continuity of the random resolvent operator associated with the random H ·, · , φ -η-accretive mappings. We introduce and study a new system of random generalized variational inclusions with random H ·, · , φ -η-accretive mappings and random fuzzy mappings in Banach spaces. By using the random resolvent operator, an iterative algorithm for solving such system of random generalized variational inclusions is constructed in Banach spaces. We prove the convergence of the iterative sequences generated by the algorithm

Introduction

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