Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property

Bruck, Ronald E.; Kuczumow, Tadeusz; Reich, Simeon

doi:10.4064/cm-65-2-169-179

Cited by 184 publications

(108 citation statements)

References 21 publications

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“…It is known that X satisfies the GGLD property if either X is UKK or X satisfies the uniform Opial condition. Under these stronger assumptions, Theorem 3(b) can be derived from results in [4] and [10]. Proof.…”

Section: We Have Proved That F Ix(f ) ⊆ F Ix(t ) On the Other Hand mentioning

confidence: 98%

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

Benavides

Ramírez²

2001

Proc. Amer. Math. Soc.

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Abstract. Let X be a Banach space, C a weakly compact convex subset of X and T : C → C an asymptotically nonexpansive mapping. Under the usual assumptions on X which assure the existence of fixed point for T , we prove that the set of fixed points is a nonexpansive retract of C. We use this result to prove that all known theorems about existence of fixed point for asymptotically nonexpansive mappings can be extended to obtain a common fixed point for a commuting family of mappings. We also derive some results about convergence of iterates.

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Section: We Have Proved That F Ix(f ) ⊆ F Ix(t ) On the Other Hand mentioning

confidence: 98%

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

Benavides

Ramírez²

2001

Proc. Amer. Math. Soc.

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“…Definition 1.5. A Banach space E has the Kadec-Klee property [8] if for every sequence {x n } in E, x n → x weakly and x n → x it follows that x n − x → 0. Let δ be the modulus of uniform convexity.…”

Section: Recall the Following Definitionsmentioning

confidence: 99%

Weak convergence theorems for nearly asymptotically nonexpansive mappings and asymptotically nonexpansive non-self mappings in uniformly convex Banach spaces

2017

Commun. Optim. Theory

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“…(iv) T is asymptotically nonexpansive in the intermediate sense [R.E.Bruck, 1993] provided T is uniformly continuous and,…”

Section: Preliminariesmentioning

confidence: 99%

Weak Convergence of Ishikawa Iteration with Error for Pseudo Contractive Mappings in Hilbert Spaces

Wu¹

2011

JMR

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Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property

Cited by 184 publications

References 21 publications

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

Weak convergence theorems for nearly asymptotically nonexpansive mappings and asymptotically nonexpansive non-self mappings in uniformly convex Banach spaces

Weak Convergence of Ishikawa Iteration with Error for Pseudo Contractive Mappings in Hilbert Spaces

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