Solving variational inequalities over solutions of split equality common fixed point problems for demicontractive mappings

Abstract

In this manuscript, we propose two average viscosity iterative schemes to approximate solutions of split equality common fixed point problems, which also address a pair of variational inequality problems governed by a broad class of demi-contractive mappings. We present examples of \(\beta \)-demicontractive mappings that are neither nonexpansive nor quasi-nonexpansive, and not strictly pseudo-contractive. The strong convergence of these methods is established in Hilbert spaces, extending and generalizing earlier studies. Numerical experiments implemented in Python are provided to illustrate the convergence of our results.