Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces

Sahu, D.R.; Petruşel, Adrian

doi:10.1016/j.na.2011.05.078

Cited by 58 publications

(37 citation statements)

References 23 publications

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“…Let p ∈ F (S) ∩ F (T ) and {α n } be a sequence in [0, 1] satisfying (i) ∞ n=1 α n = ∞, (ii) lim n→∞ α n = 0. For arbitrary x 1 ∈ C, let {x n } be a sequence iteratively defined by (13). Then the sequence {x n } converges strongly at the common fixed point p of S and T .…”

Section: Resultsmentioning

confidence: 99%

Strong Convergence for Hybrid S-Iteration Scheme of Nonexpansive and Asymptotically Demicontractive Mappings

Gopinath¹,

Gnanaraj²,

Lalithambigai³

2016

Int. J. of Pure and Appl. Math.

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Let C be a non-empty closed convex subset of real Banach space E. Let S : C → C be nonexpansive mapping and let T : C → C be a uniformly L-Lipschitizian, asymptotically demicontractive mapping with sequence{an} ⊆ [0, 1), limFor arbitrary x1 ∈ C, let {xn} be a sequence iteratively defined by xn+1 = Syn, yn = (1 − αn)xn + αnT n xn, n ≥ 1. Then we prove that the sequence {xn} converges strongly at the common fixed point p of S and T .

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Section: Resultsmentioning

confidence: 99%

Strong Convergence for Hybrid S-Iteration Scheme of Nonexpansive and Asymptotically Demicontractive Mappings

Gopinath¹,

Gnanaraj²,

Lalithambigai³

2016

Int. J. of Pure and Appl. Math.

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“…Recently, Ullah and Arshad [45] introduced the M-iteration. They proved that this iterative process converges faster than all of S [7], Picard-S [19], Picard, Mann [30], Ishikawa [26], Noor [31], SP [35], CR [17], S * [27], Abbas [4] and Normal-S [38] iteration processes. The following is the M-iteration process introduced by Ullah and Arshad [45] in 2018.…”

Section: Theorem 27 ([39]mentioning

confidence: 99%

Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

Okeke

Abbas

2020

Appl. Gen. Topol.

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It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

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“…Kirk [24], Rhoades [29] and Hussain et al [12] studied Kirk type iterative algorithms with faster convergence rate than other existing iterative algorithms. Results on S-iterative algorithm for pseudo-contractive and contractive maps, respectively, were established by Sahu and Peturasel [31] and Kumar et al [23].…”

Section: Introductionmentioning

confidence: 96%

Random iterative algorithms and almost sure stability in Banach spaces

Rahim

Kumar²,

Narwal³

et al. 2017

Filomat

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Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized φ-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

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Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces

Cited by 58 publications

References 23 publications

Strong Convergence for Hybrid S-Iteration Scheme of Nonexpansive and Asymptotically Demicontractive Mappings

Strong Convergence for Hybrid S-Iteration Scheme of Nonexpansive and Asymptotically Demicontractive Mappings

Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

Random iterative algorithms and almost sure stability in Banach spaces

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