Hybrid iterative scheme for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings

In this paper, we introduce a new mapping and a Hybrid iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common fixed point of a finite family of nonexpansive mappings which is a solution of the generalized equilibrium problem. The results obtained in this paper extend the recent ones of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69 (2008) 1025–1033].     

Convergence theorem of common fixed points for a family of nonspreading mappings in Hilbert space

We introduce the concept of K-mapping of a finite family of nonspreading mappings {T_i}_i=1^N{\{T_i\}_{i=1}^N} and we show that the fixed point set of the K-mapping is the set of common fixed points of {T_i}_i=1^N{\{T_i\}_{i=1}^N}. Moreover, we prove strong convergence theorem of the Ishikawa iterative process to a common fixed point of a finite family of nonspreading mappings in Hilbert space under certain control conditions.     

A new general system of variational inequalities for convergence theorem and application

Numerical Algorithms - In this present paper, we propose a modified form of generalized system of variational inequalities and introduce an iterative scheme for finding a common element of the set...     

A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems

In this paper, we modify the set of variational inequality to construct a new iterative scheme for finding a common element of the set of fixed point problems of infinite family of κ _i -pseudo-contractive mappings and the set of equilibrium problem and two set of variational inequality problems.