Weak and strong convergence theorems of fixed points for total asymptotically nonexpansive multi-valued mappings in Banach spaces

Na, Jing; Tang, Yong-Kun

doi:10.12988/ams.2014.42138

Cited by 4 publications

(4 citation statements)

References 11 publications

(13 reference statements)

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“…) ) for any Lemma (1.14) [10] Let be three nonnegative sequences and ) for some nonnegative integer . If ∑ ∑ exists.…”

Section: Letmentioning

confidence: 99%

Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping

Abed

2022

eijs

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In this work, we introduce Fibonacci– Halpern iterative scheme ( FH scheme) in partial ordered Banach space (POB space) for monotone total asymptotically non-expansive mapping (, MTAN mapping) that defined on weakly compact convex subset. We also discuss the results of weak and strong convergence for this scheme. Throughout this work, compactness condition of m-th iterate of the mapping for some natural m is necessary to ensure strong convergence, while Opial's condition has been employed to show weak convergence. Stability of FH scheme is also studied. A numerical comparison is provided by an example to show that FH scheme is faster than Mann and Halpern iterative schemes.

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“…) ) for any Lemma (1.14) [10] Let be three nonnegative sequences and ) for some nonnegative integer . If ∑ ∑ exists.…”

Section: Letmentioning

confidence: 99%

Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping

Abed

2022

eijs

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“…for any 11 , ( Later, many researchers introduced results on convergence of the Mann scheme and its modified versions for differe classes of mappings such as nonexpansine, pseudo-contractions, total asymptotically nonexpansive mappings ... etc. For example, see [1][2][3], [5][6], [12], [14], [18] and see [22][23], [24], [26], [31], [34], [35]. Recently, there are some convergence theorems of such a scheme in an POB (A,≾).…”

Section: Introductionmentioning

confidence: 99%

Results on a faster iterative scheme for a generalized monotone asymptotically

Abed¹,

Abed²

2021

JAM

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This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1) where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status.

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“…Recently, Alber and el at [10] introduced the class of total asymptotic non-expansive mappings which are unified various definitions of classes of nonlinear mappings. Also, Na and Tang [16] proved the set-valued version of total asymptotic non-expansive mapping and some theorems about weak and strong convergence in uniformly convex Banach spaces for two steps iterative sequence which depending on the projection mapping. Throughout this article, → and ⇀are denoted by strong convergence and weak convergence, respectively.…”

Section: Introductionmentioning

confidence: 99%

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Abed¹

2020

JAM

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The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

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Weak and strong convergence theorems of fixed points for total asymptotically nonexpansive multi-valued mappings in Banach spaces

Cited by 4 publications

References 11 publications

Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping

Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping

Results on a faster iterative scheme for a generalized monotone asymptotically

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

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