Existence results for some equilibrium problems involving Βh-monotone trifunction

The objective of this paper is to establish the existence and uniqueness of the solution of (EP) by generalizing a new class of trifunction equilibrium problems in the setting of Banach space. Furthermore, we consider trifunction as special cases of Ep(β1, β2) and find new conditions under which the equilibrium state holds using βh- monotone subsets and especially in convex and closed subsets (bounded or unbounded). In so doing, we are able to ensure the existence and uniqueness of the solution of (EP), thus improving latest properties in its literature. We are also interested in obtaining optimization as a particular case of Ep(β1, β2).