Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping Jφ for some gauge φ. Let Ti : K → K be a family of multivalued nonexpansive mappings with F := ∩∞i=0 F(Ti) ≠ ∅ which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. It is our purpose in this paper to prove the convergence of two viscosity app...

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...

In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappingsS1, S2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach space. We obtain convergence results for considered iteration to common fixed point of two asymptotically quasi-I-nonexpansive mappings, asymptotically quasi-nonexpansive mapping and equilibrium problem in frame w...

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...

the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

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...

We present several new results on the asymptotic behavior of firmly nonexpansive mappings in Banach spaces and in the Hubert ball. Let D be a subset of a (real) Banach space X. Recall that a mapping T: D -» X is said to be firmly nonexpansive [2, 4] if for each x and y in D, the convex function /: [0,1] -> [0, oo) defined by f{s) = \(\-s)x + sTx-((l-s)y + sTy) \ is nonincreasing. Note that T is...

Let A and B be nonempty subsets of a metric space X, d . Consider a mapping T : A ∪ B → A ∪ B, T is called a cyclic map if T A ⊆ B and T B ⊆ A. x ∈ A is called a best proximity point of T in A if d x, Tx d A,B is satisfied, where d A,B inf{d x, y : x ∈ A, y ∈ B}. In 2005, Eldred et al. 1 proved the existence of a best proximity point for relatively nonexpansive mappings using the notion of prox...

Let X be a uniformly convex Banach space and S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup such that F S ⋂s>0 F T s / ∅. Consider the iterative method that generates the sequence {xn} by the algorithm xn 1 αnf xn βnxn 1 − αn − βn 1/sn ∫sn 0 T s xnds, n ≥ 0, where {αn}, {βn}, and {sn} are three sequences satisfying certain conditions, f : C → C is a contraction mapping. Strong convergence of t...