Displaying similar documents to “Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces”

Strong convergence theorems of a new hybrid projection method for finite family of two hemi-relatively nonexpansive mappings in a Banach space

Kriengsak Wattanawitoon, Poom Kumam (2011)

Banach Center Publications

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In this paper, we prove strong convergence theorems of the hybrid projection algorithms for finite family of two hemi-relatively nonexpansive mappings in a Banach space. Using this result, we also discuss the resolvents of two maximal monotone operators in a Banach space. Our results modify and improve the recently ones announced by Plubtieng and Ungchittrakool [Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx....

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

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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.

The super fixed point property for asymptotically nonexpansive mappings

Andrzej Wiśnicki (2012)

Fundamenta Mathematicae

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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 note on Picard iterates of nonexpansive mappings

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

Annales Polonici Mathematici

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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...