Set-valued variational inclusion problem with fuzzy mappings involving XOR-operation

Abstract

In this paper, we introduce a set-valued variational inclusion problem with fuzzy mappings involving XOR-operation. We define a resolvent operator involving a bi-mapping and prove resolvent operator is single-valued, comparison and Lipschitz-type continuous. Based on resolvent operator we proposed an iterative algorithm to find the approximate solution of our problem. An existence and convergence result is proved for set-valued variational inclusion problem with fuzzy mappings involving XOR-operation without using the properties of a normal cone. Examples are constructed for illustration.