Common fixed point results for three and four mappings on vector-b-metric space with a graph

Hooda, Rahul; Kamra, Mamta; Malik, Archana

doi:10.1007/s12215-022-00810-2

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…and the set of edges given by the following: (1,3), (1,4), (1,5), (1,7), (1,13), (1,15), (3,2), (2,4), (5,2), (2, 7), (13,2), (2,15), (3,4), (3,5), (3,7), (3,13), (3,15), (5,4), (4,7), (13,4), (4,15), (5,7), (5,13), (5,15), (7,13), (7,15), (13,15).…”

Section: Graphical Bipolar B-mssmentioning

confidence: 99%

“…In 2019, Younis et al expanded on previous work by extending these notions to graphical rectangular b-MSs and controlled-graphical MSs [11,14]. Hooda et al [15] provided a good summary of the literature on b-MSs and their generalized forms. The authors emphasized specific ordered vector spaces derived from the b-MSs and discussed their relevance in economic research.…”

Section: Introductionmentioning

confidence: 99%

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Bipolar b-Metric Spaces in Graph Setting and Related Fixed Points

2023

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In this article, we develop a new notion that combines fixed-point theory and graph theory: graphical bipolar b-metric spaces. We demonstrate fixed-point solutions in the framework of graphical bipolar b-metric spaces, employing covariant and contravariant mapping contractions, which is a new addition to this end. This article also features illustrative examples drawn from various contexts to further demonstrate our findings. This is a significant study since it melds ideas from graph theory with those from generalized bipolar metric spaces, and considers that the symmetry of the edges of the underlying graphs connected with the enunciated metric spaces is essential in the graphical metric spaces.

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Section: Graphical Bipolar B-mssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bipolar b-Metric Spaces in Graph Setting and Related Fixed Points

2023

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Nonlinear contractions on directed graphs with applications to boundary value problems

Filali,

Akram,

Dilshad

2024

MATH

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<abstract><p>This article contains some outcomes on fixed points for a graph preserving nonlinear contraction in a metric space endued with a transitive directed graph. Our results improved, enriched, and subsumed various known fixed point theorems. To argue for reliability of our results, we presented two examples. We concluded the manuscript to investigate a unique solution of a certain first-order boundary value problem by means of our results.</p></abstract>

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Common fixed point results for three and four mappings on vector-b-metric space with a graph

Cited by 2 publications

References 42 publications

Bipolar b-Metric Spaces in Graph Setting and Related Fixed Points

Bipolar b-Metric Spaces in Graph Setting and Related Fixed Points

Nonlinear contractions on directed graphs with applications to boundary value problems

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