Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

Khan, Arshad Ali; Ali, Basit

doi:10.3390/sym13112206

Cited by 5 publications

(2 citation statements)

References 34 publications

(42 reference statements)

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“…The "Completeness Problem" is equivalent to another problem in Behavioral Sciences known as the "End Problem" (see [32]). Completeness characterizations have further been studied in connection with best proximity points [33,34]. for all k ≥ j ≥ h n .…”

Section: Completeness Of F −Metric Spaces Via the Best Proximity Pointsmentioning

confidence: 99%

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

et al. 2023

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In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F−metric spaces. Further, we obtain the best proximity point result for generalized α−φ−proximal contractions in F−metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F−metric spaces via best proximity points.

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Section: Completeness Of F −Metric Spaces Via the Best Proximity Pointsmentioning

confidence: 99%

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

et al. 2023

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“…The theorems have ensured fixed point existence and uniqueness with functions defined to complete space and contractive function [4]. The theory of fixed point has a significant role in solving the problems in mathematics, i.e., linear equations, differential equations (ordinary and partial), and integral equations [5]. Fixed point theory has also helped solve problems in other scopes such as biology, physics, chemistry, economics, programming, and electronic engineering [6].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces

Idrus

Resmawan

Payu

et al. 2022

InPrime:Ind.Jour.Pure.Applied.Math

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The fixed point theory remains the most important and preferred topic studied in mathematical analysis. This study discusses sufficient conditions to prove a unique fixed point in quasi-αb-metric spaces with cyclic mapping. The analysis starts by showing fulfillment of the cyclic Banach contraction and proving the Cauchy sequence as a condition for proving a unique fixed point in quasi-αb-metric spaces with cyclic mapping. Furthermore, it's shown that the cyclic mappings, T have a unique fixed point in quasi-αb-metric spaces. Finally, an example is given to strengthen the proof of the theorems that have been done.Keywords: fixed point theory; Quasi -Metric spaces; Cyclic Banach Contraction; Cauchy sequence. AbstrakTeori titik tetap termasuk salah satu topik penting dan menarik untuk diteliti pada bidang analisis. Pada penelitian ini, dibahas tentang syarat cukup dalam membuktikan bahwa terdapat titik tetap tunggal dalam ruang quasi- b-metrik pada pemetaan siklik. Analisis diawali dengan menunjukkan pemenuhan kondisi kontraksi Banach siklik dan pembuktian barisan Cauchy sebagai syarat pembuktian bahwa terdapat titik tetap tunggal pada pemetaan siklik dalam ruang quasi- b-metrik. Selanjutnya ditunjukkan bahwa pemetaan siklik memiliki titik tetap tunggal dalam ruang quasi b-metrik. Terakhir, diberikan contoh untuk memperkuat pembuktian teorema yang telah dilakukan.Kata Kunci: teori titik tetap; ruang Quasi -Metrik; Kontraksi Banach Siklik; barisan Cauchy.

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Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

2023

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This paper deals with the existence of an optimum solution of a system of ordinary differential equations via the best proximity points. In order to obtain the optimum solution, we have developed the best proximity point results for generalized multivalued contractions of b-metric spaces. Examples are given to illustrate the main results and to show that the new results are the proper generalization of some existing results in the literature.

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Completeness of b−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions

Cited by 5 publications

References 34 publications

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

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