Mixed Equilibrium Problems with Weakly Relaxedα-Monotone Bifunction in Banach Spaces

Monotone Bifunction ◽

We introduce the class of mixed equilibrium problems with the weakly relaxedα-monotone bi-function in Banach spaces. Using the KKM technique, we obtain the existence of solutions for mixed equilibrium problem with weakly relaxedα-monotone bi-function in Banach spaces. The results presented in this paper extend and improve the corresponding results in the existing literature.

New Mixed Equilibrium Problems and Iterative Algorithms for Fixed Point Problems in Banach Spaces

Journal of Applied Mathematics ◽

10.1155/2014/193749 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Minjiang Chen ◽

Jianmin Song ◽

Shenghua Wang

Keyword(s):

Equilibrium Problem ◽

Banach Spaces ◽

Equilibrium Problems ◽

Existence Of Solutions ◽

Monotone Mapping ◽

Iterative Algorithms ◽

Common Element ◽

We first introduce a new mixed equilibrium problem with a relaxed monotone mapping in Banach spaces and prove the existence of solutions of the equilibrium problem. Then we introduce a new iterative algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a quasi-ϕ-nonexpansive mapping and prove some strong convergence theorems of the iteration. Our results extend and improve the corresponding ones given by Wang et al., Takahashi and Zembayashi, and some others.

On Mixed Equilibrium Problems in Hadamard Spaces

Journal of Mathematics ◽

10.1155/2019/3210649 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Chinedu Izuchukwu ◽

Kazeem Olalekan Aremu ◽

Olawale Kazeem Oyewole ◽

Oluwatosin Temitope Mewomo ◽

Safeer Hussain Khan

Keyword(s):

Equilibrium Problem ◽

Resolvent Operator ◽

Equilibrium Problems ◽

Existence Of Solution ◽

Proximal Point ◽

Unique Existence ◽

Mixed Equilibrium ◽

The Resolvent Operator

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

THE EXISTENCE OF SOLUTIONS AND WELL-POSEDNESS FOR BILEVEL MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

Taiwanese Journal of Mathematics ◽

10.11650/tjm.17.2013.2337 ◽

2013 ◽

Vol 17 (2) ◽

pp. 725-748 ◽

Cited By ~ 11

Author(s):

Jia-wei Chen ◽

Yeol Je Cho ◽

Zhongping Wan

Keyword(s):

Banach Spaces ◽

Equilibrium Problems ◽

Existence Of Solutions ◽

Well Posedness ◽

Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Journal of Applied Mathematics ◽

10.1155/2012/859492 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21

Author(s):

Rabian Wangkeeree ◽

Hossein Dehghan ◽

Pakkapon Preechasilp

Keyword(s):

Strong Convergence ◽

Equilibrium Problem ◽

Banach Spaces ◽

Nonexpansive Mappings ◽

Finite Family ◽

Generalized Mixed Equilibrium Problem ◽

Asymptotically Nonexpansive ◽

Generalized Mixed Equilibrium ◽

We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.