and Applied Analysis 3 for all x, y ∈ C. A mapping A : C → H is said to be α-inverse strongly g-monotone if and only if 〈 Ax −Ay, g x − gy ≥ α∥Ax −Ay∥2, 2.2 for some α > 0 and for all x, y ∈ C. A mapping g : C → C is said to be strongly monotone if there exists a constant γ > 0 such that 〈 g x − gy, x − y ≥ γ∥x − y∥2, 2.3 for all x, y ∈ C. Let B be a mapping ofH into 2 . The effective domain of...

In this paper, we investigate the split variational inequality problem in Hilbert spaces, which an operator is ?-inverse strongly ?-monotone and another pseudomonotone. We construct iterative algorithm for solving problem. show strong convergence of suggested algorithm.

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber’s inequalities, Nalder’s results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear oper...

In this paper, we introduce regularization methods for finding a point, being not only solution monotone variational inequality problem but also common zero an infinite family of inverse strongly non-self operators closed convex subset in real Hilbert space. these methods, finite number the is used at each iteration step. Applications to fixed point strictly pseudo-contractive and split feasibi...

In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generat...

In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09...

We introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for nonexpansive semigroup, and the set of solutions of the quasi-variational inclusion problem with multivalued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some str...

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse stronglymonotonemappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated...