this paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   the main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

Let C be a nonempty closed bounded convex subset of a Banach space X whose characteristic of noncompact convexity is less than 1 and T a continuous 1-χ-contractive SL map (which is not necessarily nonexpansive) from C to KC(X) satisfying an inwardness condition, where KC(X) is the family of all nonempty compact convex subsets of X . It is proved that T has a fixed point. Some fixed points resul...

Abridged English Version – Let (Ti)i∈I be a countable family of firmly nonexpansive mappings on a real Hilbert space H [i.e., (1) holds] and let F denote their set of common fixed points, which is assumed to be nonempty. In this Note we consider the problem (P) of finding a point in F . This generic problem arises in many branches of applied mathematics, e.g., solving systems of variational ine...

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

T h e homotopic invariance of fixed points of set-valued contractions and nonexpansive mappings is studied. As application, nonlinear alternative principles are given. A LeraySchauder alternative and an antipodal theorem for set-valued nonexpansive mappings are also included.

We discuss the concept of probabilistic quasi-nonexpansive mappings in connection with the mappings of Nishiura. We also prove a result regarding the convergence of the sequence of successive approximations for probabilistic quasi-nonexpansive mappings.

In this paper, we prove some strong convergence approximation theorems of strongly relatively nonexpansive semi-group in the framework of Banach spaces. Using the concept of duality theorems, we obtain analogue results for strongly generalized nonexpansive semi-group and for semi-group of firmly generalized nonexpansive type. The results presented in this paper improve and extend some correspon...

Using Cesàro means of a mapping, we modify the progress of Mann’s iteration in hybrid method for asymptotically nonexpansive mappings in Hilbert spaces. Under suitable conditions, we prove that the iterative sequence converges strongly to a fixed point of an asymptotically nonexpansive mapping. We also introduce a new hybrid iterative scheme for finding a common element of the set of common fix...

The main purpose of this paper is to study an iteration procedure for finding a common fixed point of a countable family of nonexpansive mappings in Banach spaces. We introduce a Mann type iteration procedure. Then we prove that such a sequence converges weakly to a common fixed point of a countable family of nonexpansive mappings. Moreover, we apply our result to the problem of finding a commo...