A common solution of split equality monotone inclusion problem and split equality fixed point problem in real Banach spaces

Abstract

In this paper, we introduce an iterative algorithm for approximating a common solution of Split Equality Monotone Inclusion Problem (SEMIP) and Split Equality Fixed Point Problem (SEFPP) in p-uniformly convex Banach spaces which are also uniformly smooth. Under standard and mild assumptions of monotonicity and right Bregman strongly condition of the SEMIP- and SEFPP-associated mappings, we establish the strong convergence of the scheme. Finally, we applied our result to study the convex minimization problem (CMP) and Equilibrium Problem. Our result complements and extends some recent results in literature.