Some results of trifunction equilibrium problem

The objective of this thesis is to investigate in a rigorous manner a number of equilibrium problems resulting from applied sciences. Put differently, the thesis is the study of equilibrium problems in Banach space and reflexive Banach space with the aim of obtaining results on the existence of solutions of equilibrium problems in the case of convex and bounded subsets by using a KKM mapping, compactness and convex function. To do so, the thesis is composed of five chapters. Chapter two recalls a family of essential definitions along with some Theorems. The aim of this chapter is to assist the reader to get acquainted with main results grounded thereof. Chapter three is planned to found novel results of existence and uniqueness for GEp (T,ϑ_1,ϑ_2 ) generalizing a new class of trifunction equilibrium problems, with a novel type of monotonicity in Banach space. Chapter four is intended to prove that the issues of well-posedness for GEp_t (〖T,ϑ〗_1,ϑ_2 ) which is corresponding to the existence and uniqueness of its solution. Among the important results that we obtained, under specific conditions, we were able to prove that if GEp_t (〖T,ϑ〗_1,ϑ_2 ) is WP. Then, Ξ(c)≠∅ and 〖lim 〗_(c→0) diam [Ξ(c)]=0, where known in the same chapter. The hoped-for results in this thesis is aimed to renew and improve some corresponding solutions of several researchers.