Some results of equilibrium problems involving pseudo-monotone bifunction

The hypothetical of Equilibrium Problems (EP) has found its applications in different offshoot of non-linear sciences. The subgradient projection method, which is a continuation of the steepest descent projection method in smooth optimization, is a crucial strategy for resolving equilibrium problems. It is common knowledge that when the bi-fun f is convex subdifferentiable due to the 2nd argument and lipschitz, strongly monotone on K, one can select regularization parameters such that this technique linearly converges. The primary goal of this thesis is to determine some outcomes for new class of equilibrium problem (for short EP) involving pseudomonotonicity bi-fun by using KKM technique, whose outcome is sought in a subset K of a Banach space X. This thesis consists of five chapters, chapters two and three contain a set of basic approach along with some theories. The aim of these two chapters is to help the reader to get the gettings we will reach in this thesis. In the fourth chapter, we discuss a novel idea known as pseudo-monotone and present some existence results of solutions for the problem (IEP). In addition to this, we investigate the implications of applying (IEP) to hemivariational inequalities and well-posedness. Among the main outcomes that were introduced in this thesis : Assume that f:K×K→R be relaxed α-β-η-pseudo-monotone and let K be a non-empty subset of Banach space X, under some assumptions. Then, the (IEP) is equivalent to the f(ϑ,η(υ ̅,ϑ))≤α(η(ϑ,υ ̅ ))+β(ϑ,υ ̅ ).