Stability results for Jungck-type iterative processes in convex metric spaces

The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.

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“…Journal of Function Spaces Putting = = 1 in (N), we get well known Mann iteration [21,22] in convex metric spaces:…”

Section: (N)mentioning

confidence: 99%

On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces

Chugh

Malik

Kumar³

2015

Journal of Function Spaces

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“…A lot of authors generalized this scheme to Jungck-Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-SP, these iterations used to approximate the common fixed point for mappings under suitable contractive condition see [1,4,10,11,12,15,19,20,22,24]. The first stability result on T -stable mappings was given by Ostrowaski [26] where he proved the stability of the Picard iteration under Banach contraction condition while Osilike et al [25] improved this result on (S, T )-stable as follows:…”

Section: Introductionmentioning

confidence: 99%

Stability and Strong Convergence Results for Random Jungck-Kirk-Noor Iterative Scheme

Rashwan

Hammad

2017

Fasciculi Mathematici

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Abstract. The purpose of this study is to introduce a JungckKirk-Noor type random iterative scheme and prove stability and strong convergence of this to establish a general theorem to approximate the unique common random coincidence point for two or more nonself random commuting mappings under general contractive condition in various spaces. Also we give the stability and convergence for random Jungck-Kirk-Ishikawa and random Jungck-Kirk-Mann as a corollaries. The results obtained in this paper improve the corresponding results announced recently.

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“…On the other hand, stability results established in metric spaces and normed linear spaces have been studied by several mathematicians such as Haghi et al [10], Olatinwo and Postolache [14]. Therefore, the stability of iteration scheme (S n ) still open for interested mathematicians.…”

Section: Conclusion and Open Problemmentioning

confidence: 99%

On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis

Sintunavarat¹,

Pitea²

2016

J. Nonlinear Sci. Appl.

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The aim of this work is to introduce a new three step iteration scheme for approximating fixed points of the nonlinear self mappings on a normed linear spaces satisfying Berinde contractive condition. We also study the sufficient condition to prove that our iteration process is faster than the iteration processes of Mann, Ishikawa and Agarwal, et al. Furthermore, we give two numerical examples which fixed points are approximated by using MATLAB.

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Stability results for Jungck-type iterative processes in convex metric spaces

Cited by 40 publications

References 10 publications

On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces

On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces

Stability and Strong Convergence Results for Random Jungck-Kirk-Noor Iterative Scheme

On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis

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