STRONG CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITY PROBLEMS AND SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS

Abstract. In this paper, we construct a new iterative scheme by hybrid method for approximation of common element of set of solutions of a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the two sets. We give several applications of our results in a Banach space. Our results extend many important recent results in the literature

Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

Let {Ti}i=1N be N strictly pseudononspreading mappings defined on closed convex subset C of a real Hilbert space H. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality 〈(γf-μB)x*,v-x*〉≤0, ∀v∈⋂i=1NFix(Ti)

Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

Let {T i } N i 1 be N strictly pseudononspreading mappings defined on closed convex subset C of a real Hilbert space H. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality γf − μB x * , v − x * ≤ 0, ∀v ∈ N i 1 F ix T i

A strong convergence theorem on generalized equilibrium problems and strictly pseudocontractive mappings

Abstract. In this paper, we consider a general iterative process for a generalized equilibrium problem and a strictly pseudocontractive mapping. A strong convergence theorem of common elements of the fixed point sets of the strictly pseudocontractive mapping and of the solution sets of the generalized equilibrium problem is established in the framework of Hilbert spaces

A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature

Iterative Methods for Family of Strictly Pseudocontractive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of -strictly pseudocontractive mappings and the set of common solutions to a system of generalized mixed equilibrium problems and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three above described sets. We give an application of our results. Our results extend important recent results from the current literature.</p