Multivalued $F$-contractive mappings with a graph and some fixed point results

Acar, Özlem; Altun, İshak

doi:10.5486/pmd.2016.7308

Cited by 21 publications

(21 citation statements)

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“…Jachymski [1] gave a unified version of Banach's contraction principle, by considering the graph structure instead of an order structure on a metric space. This result has been extended and generalized by many researchers in different ways (see, e.g., [2][3][4][5][6][7][8][9][10][11]). Recently, Shukla et al in [10] proposed the notion of graphical metric spaces as a graphical version of metric spaces.…”

Section: Introductionmentioning

confidence: 92%

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

Younis

Singh

Petruşel

2019

Discrete Dynamics in Nature and Society

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The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphical b-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

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Section: Introductionmentioning

confidence: 92%

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

Younis

Singh

Petruşel

2019

Discrete Dynamics in Nature and Society

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“…[2] (see also [3]) modified the concept of -contractions via -admissibility. Many authors have formed different generalizations of Wardowski [1] result (see [4][5][6]). Recently, in [7] authors provided a fixed point result for aĆirić type -contraction.…”

Section: Introductionmentioning

confidence: 99%

Existence of Fixed Points of Four Maps for a New Generalized F-Contraction and an Application

Nazam

Aydi

Noorani

et al. 2019

Journal of Function Spaces

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“…So the concept of an F -contraction proved to be a milestone in fixed point theory. Numerous research papers on Fcontractions have been published (see for instant [5,6,11,15,17]). Recently, Minak et al [13] presented a fixed point result for Círíc type generalized F -contraction.…”

Section: Introductionmentioning

confidence: 99%

On Common Fixed Points Theorems for Ordered $F$-Contractions With Application

Nazam

Acar

2018

FU Math Inform

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We study the conditions for existence of a unique common fixed point of ordered $F$-contractions defined on an ordered partial metric space; in particular, we present a common fixed point result for a pair of ordered $F$-contractions satisfying a generalized rational type contractive condition and discuss its consequences. It is remarked that the notion of an $F$-contraction in partial metric spaces is more general than that in metric spaces. As application of our findings, we demonstrate the existence of common solution of the system of Volterra type integral equations.

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Multivalued $F$-contractive mappings with a graph and some fixed point results

Cited by 21 publications

References 0 publications

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

Existence of Fixed Points of Four Maps for a New Generalized F-Contraction and an Application

On Common Fixed Points Theorems for Ordered $F$-Contractions With Application

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