Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups

“…In [16], it is point out that there exist uniformly convex Banach spaces which have neither a Fréchet differentiable norm nor the Opial property but their duals do have the Kadec-Klee property. And the duals of reflexive Banach spaces with Fréchet differentiable norms or the Opial property have the Kadec-Klee property.…”

Section: This Implies That Limmentioning

confidence: 99%

A new two step iterative scheme for a finite family of nonself I-asymptotically nonexpansive mappings in Banach space

Gunduz¹

2017

ntmsci

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Let E be a real uniformly convex Banach space, K be a nonempty closed convex subset of E and let T i : K → E be N I i -asymptotically nonexpansive nonself mappings and I i be N asymptotically nonexpansive nonself mappings. It is proved that a new two step iterative algorithm converges weakly to a q ∈ F in a real uniformly convex Banach space such that its dual has the Kadec-Klee property and strongly under condition (B) in a real uniformly convex Banach space. It presents some new results in this paper.

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“…Lemma 2.5. (See [11]) Let E be a real reflexive Banach space with its dual E * has the Kadec-Klee property. Let {x n } be a bounded sequence in E and p, q ∈ w w (x n ) (where w w (x n ) denotes the set of all weak subsequential limits of {x n }).…”

Section: Lemma 23 (Seementioning

confidence: 99%

Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces

Saluja¹

2014

J. Nonlinear Sci. Appl.

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The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial's condition or the dual E * of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the existing literature. c 2014 All rights reserved.Keywords: Asymptotically quasi-nonexpansive non-self mappings, common fixed point, the modified two-step iteration process with errors for non-self maps, uniformly convex Banach space, weak convergence. 2010 MSC: 47H09, 47H10, 47J25.

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Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups

Cited by 44 publications

References 16 publications

Weak and strong convergence of finite family with errors of nonexpansive nonself-mappings

Weak and strong convergence of finite family with errors of nonexpansive nonself-mappings

A new two step iterative scheme for a finite family of nonself I-asymptotically nonexpansive mappings in Banach space

Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces

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