Fixed Point Results for α*-ψ-Dominated Multivalued Contractive Mappings Endowed with Graphic Structure

Rasham, Tahair; Shoaib, Abdullah; Alamri, Badriah A. S.; Asif, Awais; Arshad, Muhammad

doi:10.3390/math7030307

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…Hussain et al [12], introduced the concept of graphic contractions and obtained a point fixed result. Further results on graphic contraction can be seen in [8,21,27]. Shang [25], discussed briefly basic notions of graph limit theory and fix some necessary notations and presented many interesting applications.…”

Section: Fixed Points For Graphic Contractionsmentioning

confidence: 99%

Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

2019

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Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

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Section: Fixed Points For Graphic Contractionsmentioning

confidence: 99%

Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

2019

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“…After Banach presented his renowned Banach Contraction Principle, his idea was generalized by various authors into many interesting generalizations (see [1][2][3][4][5][6][7][8]). Wardowski [9] extended his idea to a more generalized form which he named as F-contraction.…”

Section: Introductionmentioning

confidence: 99%

3D Dynamic Programming Approach to Functional Equations with Applications

Asif

Khan

Abdeljawad

et al. 2020

Journal of Function Spaces

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This article demonstrates the graphical existence of a single fixed point while imposing the contractive condition of Chatterjea type F-contraction on F-metric space (briefly as F-MS). We present two examples that verify the validity of the results given in the paper. The paper further explains the subsistence of the fixed point even if the contractive condition is valid only for a closed ball inside the space rather than imposing it on the whole F-MS. Moreover, the application of the mentioned results in finding a single solution of functional equations is described that is widely used in computer programming and optimization.

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“…(1.1) converges to the unique fixed point. In the last few decades, many authors have extended this result by considering a more generalized space, altering the condition of the contraction or by considering different iteration processes (one may refer to [6]- [8], [9], [10], [13], [14], [19], [21]- [24], [26], [27], [28], [34], [29]- [33] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

An Extended S-Iteration Scheme for G-Contractive Type Mappings in b-Metric Spaces with Graph

Goswami¹,

Haokip²,

Mishra

2020

ijaa

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In this paper, we introduce an extended S-iteration scheme for G-contractive type mappings and prove ∆-convergence as well as strong convergence in a nonempty closed and convex subset of a uniformly convex and complete b-metric space with a directed graph. We also give a numerical example in support of our result and compare the convergence rate between the studied iteration and the modified S-iteration.

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Fixed Point Results for α*-ψ-Dominated Multivalued Contractive Mappings Endowed with Graphic Structure

Cited by 9 publications

References 18 publications

Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

3D Dynamic Programming Approach to Functional Equations with Applications

An Extended S-Iteration Scheme for G-Contractive Type Mappings in b-Metric Spaces with Graph

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