New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces

New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalizedmixed equilibriumproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed ...

Approximating fixed points for nonexpansive mappings and generalized mixed equilibrium problems in Banach spaces

We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...

Generalized Equilibrium Problem with Mixed Relaxed Monotonicity

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.

Existence and Iterative Approximation Methods for Generalized Mixed Vector Equilibrium Problems with Relaxed Monotone Mappings

We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings