We combine a sequence of contractive mappings {fn} and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. O...

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive m...

Let C be a nonempty closed convex subset of a Hilbert spaceH, T a self-mapping of C. Recall that T is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. Construction of fixed points of nonexpansive mappings via Mann’s iteration 1 has extensively been investigated in literature see, e.g., 2–5 and reference therein . But the convergence about Mann’s iteration and Ishikawa’s iterati...

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. It is assumed throughout the paper that T is a nonexpansive mapping such that F(T) =∅. One classical way to study nonexpansive mappings is to use contractions to approximate a nonexpansive mapping [1, 9]. More precisely, take t ∈ (0,1) and define a contraction Tt :...

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

We discuss the equilibrium problem for a continuous bifunction over the fixed point set of a firmly nonexpansive mapping. We then present an iterative algorithm, which uses the firmly nonexpansive mapping at each iteration, for solving the problem. The algorithm is quite simple and it does not require monotonicity and Lipschitz-type condition on the equilibrium function. At the end of the paper...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

Abstract This paper is devoted to the study of a class generalized nonexpansive mappings called nearly asymptotically and show that it properly includes mappings. We investigate problem approximating common element set solutions system nonlinear variational-like inclusions involving P - η -accretive fixed points mapping. To this end, we suggest new iterative algorithm with mixed errors. As an a...

Abstract In this paper, we study the existence of solution generalized equilibrium problem (GEP) in framework an Hadamard manifold. Using KKM lemma, prove GEP and give properties resolvent function associated with under consideration. Furthermore, introduce iterative algorithm for approximating a common fixed point problem. proposed method, obtain strong convergence theorem GEP, which is also n...

This study aims at investigation of a generalized variational inequality problem. We initiate new iterative algorithm and examine its convergence analysis. Using this newly proposed method, we estimate the common solution problem fixed points nonexpansive mapping. A numerical example is illustrated to verify our existence result. Further, demonstrate that considered converges with faster rate t...