Displaying similar documents to “Some Remarks On The Fixed Point Stability For Nonexpansive Mappings”

The super fixed point property for asymptotically nonexpansive mappings

Andrzej Wiśnicki (2012)

Fundamenta Mathematicae

Similarity:

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.

A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings

Sławomir Borzdyński, Andrzej Wiśnicki (2014)

Studia Mathematica

Similarity:

It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.

Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings

Kittipong Sitthikul, Satit Saejung (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.

Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets

Nuttawut Bunlue, Suthep Suantai (2018)

Archivum Mathematicum

Similarity:

In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive...

A note on Picard iterates of nonexpansive mappings

Eun Suk Kim, W. A. Kirk (2001)

Annales Polonici Mathematici

Similarity:

Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions...

On the fixed points of nonexpansive mappings in direct sums of Banach spaces

Andrzej Wiśnicki (2011)

Studia Mathematica

Similarity:

We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.