Solving split equality equilibrium and fixed point problems in Banach spaces
Optimization Eruditorum, Volume 1, Issue 1, June 2024, Pages 17–44
OLUWATOSIN TEMITOPE MEWOMO
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4001, South Africa
TIMILEHIN OPEYEMI ALAKOYA
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4001, South Africa
ADEOLU TAIWO
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4001, South Africa
AVIV GIBALI
Department of Applied Mathematics, HIT-Holon Institute of Technology, 5810201 Holon, Israel
Abstract
In this paper, we introduce a new algorithm for approximating a common solution of Split Equality Generalised Mixed Equilibrium Problem (SEGMEP) and Split Equality Fixed Point Problem (SEFPP) for two infinite families of closed uniformly \(L_i\)-Lipschitz continuous and \(K_i\)-Lipschitz continuous and uniformly quasi-\(\phi\)-asymptotically nonexpansive mappings (\(i \in N\) and \(\phi\) is the Lyapunov functional) in Banach spaces. Under standard and mild assumption of monotonicity and lower semicontinuity of the SEGMEP associated mappings, we establish the strong convergence of the scheme without imposing any compactness type conditions on either the operators or the spaces considered. We apply our result to approximate the solution of Split Equality Convex Minimization Problem (SECMP) and Split Equality Variational Inclusion Problem (SEVIP). A numerical example is presented to illustrate the performance and implementability of our method. Our results extend, generalize and complement several related works in the literature.
Cite this Article as
Oluwatosin Temitope Mewomo, Timilehin Opeyemi Alakoya, Adeolu Taiwo and Aviv Gibali, Solving split equality equilibrium and fixed point problems in Banach spaces, Optimization Eruditorum, 1 (2024), 17–44