In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical re...

Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0, and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B andW be maximal monotone operators on H such that the domains of B andW are included in C. Let 0 < k < 1, and let g be a k-contraction of H into itself. Let V be a γ -strongly monoto...

This paper aims at studying the convergence of some iteration processes for mixed variational inequalities with convex nondifferentiable functionals and J -potential, J -coercive, J -pseudomonotone or J -strongly inverse monotone operators in uniformly smooth Banach spaces. Our results generalize corresponding theorems of [I.B. Badriev, O.A. Zadvornov, A decomposition method for variational ine...

and Applied Analysis 3 (b) η-strongly monotone if there exists a constant η > 0 such that ⟨Sx − Sy, x − y⟩ ≥ η 󵄩󵄩󵄩󵄩x − y 󵄩󵄩󵄩󵄩 2 , ∀x, y ∈ C; (12) (c) α-inverse-strongly monotone (α-ism) if there exists a constant α > 0 such that ⟨Sx − Sy, x − y⟩ ≥ α 󵄩󵄩󵄩󵄩Sx − Sy 󵄩󵄩󵄩󵄩 2 , ∀x, y ∈ C. (13) Obviously, if S is α-inverse-strongly monotone, then it is monotone and (1/α)-Lipschitz continuous. It can be ...

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-φ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of...