Journal of Prime Research in Mathematics

# On Split Equilibrium and Fixed Point Problems for Finite Family of Bregman Quasi-Nonexpansive Mappings in Banach spaces

H. A. Abass$$^{a,*}$$, O. K. Narain$$^b$$, K. O. Oyewole$$^c$$,U. O. Adiele$$^d$$

$$^a$$School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa and DSI-NRF Centre of Excellence in   Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa.

$$^b$$ School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa.

$$^c$$ School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa.

$$^d$$ Department of Mathematics, University of North Texas, U.S.A.

Correspondence should be addressed to: hammedabass548@gmail.com

### Abstract

In this paper, we introduce a trifunction split equilibrium problem using a generalized relaxed α-monotonicity in the framework of p-uniformly convex and uniformly smooth Banach spaces. We develop an iterative algorithm for approximating a common solution of split equilibrium problem and fixed point problem for finite family of Bregman quasi-nonexpansive mappings. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating a common solution of the aforementioned problems. Our iterative scheme is design in such a way that it does not require any knowledge of the operator norm. We display a numerical example to show the applicability of our result. Our result extends and complements some related results in literature.

#### Keywords:

Split Equilibium Problem, Bregman Quasi-Nonexpansive, Iterative scheme, Fixed point problem.