Existence of Solutions to Split Variational Inequality Problems and Split Minimization Problems in Banach Spaces

TL;DR

This paper extends the theory of split variational inequality problems from Hilbert to Banach spaces and proves the existence of solutions using fixed point and Fan-KKM theorems.

Contribution

It generalizes the existence results for split variational inequality and minimization problems to Banach spaces, employing advanced fixed point and topological methods.

Findings

Existence of solutions in Banach spaces established

Application of Fan-KKM theorem to split problems

Use of fixed point theorems on posets for solvability

Abstract

In this paper, we extend the concept of split variational inequality problems from Hilbert spaces to Banach spaces. Then we apply the Fan-KKM theorem to prove the existence of solutions to some split variational inequality problems and some split minimization problems in Banach spaces. We also apply fixed point theorems on Chain complete posets to show the solvability of some split variational inequality problems in partially ordered Banach space.