Abstract
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
Highlights
Let K : n n be a set-valued map such that K ( x), for any x ∈ n, is a closed convex set in n
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function
We follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter
Summary
Let K : n n be a set-valued map such that K ( x) , for any x ∈ n , is a closed convex set in n. The set-valued vector quasi variational inequality (SVQVI) problem associated with. M; reduces to the weak Stampacchia vector variational inequality problem ( SVVI )w studied in [2]. Motivated by the extension of VI to VVI, several researchers initiated the study of QVI for vector-valued functions, known as vector quasi variational inequalities (VQVI); see, for instance [11] [12] [13] [14].
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