In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonself-mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a commo...

Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ...

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...

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let = = {T (t) : t ∈ G} be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we provide the strong mean ergodic convergence theorem for the almost-orbit of =.

The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...