Solving Split Monotone Variational Inclusion Problem and Fixed Point Problem for Certain Multivalued Maps in Hilbert Spaces.

Ferdinard Udochukwu Ogbuisi, Oluwatosin Temitope Mewomo

Abstract

In this paper, we introduce a new iterative algorithm for approximating the common solution of Split Monotone Variational Inclusion Problem (SMVIP) and  Fixed Point Problem for multivalued strictly pseudocontractive-type mappings in real Hilbert spaces. Under standard and mild assumption of inverse strongly monotonicity and maximal and monotonicity of the SMVIP associated mappings, we establish the strong convergence of the sequence generated by our iterative algorithm. We further applied our result to solve Split Minimization Problem (SMP) and Split Variational Inequality Problem (SVIP).