Iterating Fixed Point via Generalized Mann’s Iteration in Convex <i>b</i>‐Metric Spaces with Application

Asif, Awais; Alansari, Monairah; Hussain, Nawab; Arshad, Muhammad; Ali, Amjad

doi:10.1155/2021/8534239

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…Many researchers have studied this topic because it has many applications. Related to this matter, we suggest the recent literature [29][30][31][32][33][34][35] and the references therein.…”

Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 94%

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Hussain¹,

Alsulami²,

Alamri³

2023

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with S λ and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results.

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Section: Application To Nonlinear Fractional Differential Equationmentioning

confidence: 94%

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Hussain¹,

Alsulami²,

Alamri³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…Very recently, Chen et al [21] introduced the notion of a convex b − metric space and extend Mann's algorithms directly to b − metric spaces. After that, Asif et al [22] investigate fixed point of single-valued Hardy-Roger's type F − contraction globally as well as locally in a convex b − metric space. Along the line, Chen et al [23] introduce the concept of a convex graphical rectangular b − metric space and prove some fixed point theorems in this space.…”

Section: Introductionmentioning

confidence: 99%

“…Along the line, Chen et al [23] introduce the concept of a convex graphical rectangular b − metric space and prove some fixed point theorems in this space. New some fixed point results on a closed ball can be seen in [22,[24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results on Closed Ball in Convex Rectangular $b -$ Metric Spaces and Applications

Cui

Chen

2022

Journal of Function Spaces

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In this paper, the concept of convex rectangular b − metric spaces is introduced as a generalization of both convex metric spaces and rectangular b − metric spaces. The purpose of this study is to indicate a way of generalizing Mann’s iteration algorithm and a series of fixed point results in rectangular b − metric spaces. Furthermore, certain examples are given to support the results. We also study well posedness of fixed point problems of some mappings in convex rectangular b − metric spaces, and an application to the dynamic programming is entrusted to manifest the viability of the obtained results. Our results extend comparable results in the existing literature.

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Some Fixed Point Results in Function Weighted Metric Spaces

Asif

Hussain

Alsulami

et al. 2021

Journal of Mathematics

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After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of ℱ -metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of ℱ -metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole ℱ -metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole ℱ -metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.

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Iterating Fixed Point via Generalized Mann’s Iteration in Convex b‐Metric Spaces with Application

Cited by 6 publications

References 23 publications

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Fixed Point Results on Closed Ball in Convex Rectangular $b -$ Metric Spaces and Applications

Some Fixed Point Results in Function Weighted Metric Spaces

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Iterating Fixed Point via Generalized Mann’s Iteration in Convex b‐Metric Spaces with Application

Cited by 6 publications

References 23 publications

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Fixed Point Results on Closed Ball in Convex Rectangularb−Metric Spaces and Applications

Some Fixed Point Results in Function Weighted Metric Spaces

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Product

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Fixed Point Results on Closed Ball in Convex Rectangular $b -$ Metric Spaces and Applications