In this article, we introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-asymptotically nonexpansive mappings, the set of the variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for...

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

In this paper, we introduce a new iterative sequence which is constructed by using the hybrid projection method for solving the common solution for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain the conditions, the common solution for the families of quasi -φasymptotically nonexpansive and uniformly Lipschitz con...

In this paper, we introduce the iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain the sequence converges strongly to a common element of two sets. The results extended and improved the corresponding results of Plubtieng and Punpaeng [S. Plubtieng, R. ...

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by C. E. Chidume and E. U. Ofoedu, 2009 . We construct examples of total asymptotically nonexpansive mappings which are not asym...

1 School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China 2 Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea 3 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA 4 Mathematics and Statistics Department, King Fahd Univer...