Weakly absolute summability theorems and its application to find schauder basis solution of vector variational inequalities in quasi-reflexive contractible topological vector space

Abstract

The main goal of this paper is to define a contractible topological vector space in quasi-reflexive space modeled in a non-reflexive Banach space and to study the convergence of generalized vector variational inequalities and generalized vector comple-mentarity problems using weakly absolute summability theorem in it. We obtained an unconditional Schauder basis from a ?-idempotent infinite dimensional real or complex matrix developed by Das and Behera [6] and from this basis set, we obtained the solution of the problem (GVVIP). The existence of solution of the dual problem (GDVVIP), and generalized vector complementarity problem (GVCP) are established using weakly absolute almost summability theorems and vector univalent function.