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

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.