A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

Recommended by Pavel Drabek We construct implicit random iteration process with errors for a common random fixed point of a finite family of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces. The results presented in this paper extend and improve the corresponding results of Beg and Abbas in 2006 and many others.

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...

The purpose of this paper is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The method of the proof is different from the original one. Our results improve and extend the corresponding results announced by Zhou et al. 2010, Kimura and Takahashi 2009, and some others.

We prove that any Banach space X whose Banach-Mazur distance to a Hilbert space is less than √ 5+ √ 13 2 has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of a Banach space X . A mapping T : C → C is said to be nonexpansive if ‖T x− T y‖ ≤ ‖x− y‖ for any x, y ∈ C. A nonempty weakly compact convex set C is said to have the fixed point property if ev...

It is proved that Kuhfittig iteration process converges to a common fixed point of a finite family of quasi-nonexpansive maps on a Banach space. This result is extended to the random case. Our work improves upon several well-known results in the current literature.

In this paper, we introduce a class of total quasi-φ-asymptotically nonexpansive nonself mappings which contain several kinds of mappings as its special cases, and obtain some strong convergence theorems for this type of mappings in Banach spaces under some mild control conditions. The results presented in this paper improve and extend some recent corresponding results.

Strong convergence of a new iterative process based on the Shrinking projection method to a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the solution set of an equilibrium problem in a Banach space is established. Our results improved and extend the corresponding results announced by many others.