Graphic Contraction Mappings via Graphical b-Metric Spaces with Applications

Chuensupantharat, Nantaporn; Chauhan, Varsha; Singh, Deepak; Menon, Radhika

doi:10.1007/s40840-018-0651-8

Cited by 19 publications

(30 citation statements)

References 14 publications

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“…We proved that every Reich type contraction is Reich-graph contraction but the inverse implication is not true in general. We obtained the fixed point result by dropping the property S as used in [7,24]. Obtained results are validated by appropriate examples endowed with suitable graphs.…”

Section: Discussionmentioning

confidence: 99%

“…For a sequence {x m } ∈ Y if (x m , Px m+1 ) G for all m ∈ N, we say {x m } to be a G-termwise connected (in short G-TWC) sequence. Recently in a paper [7], authors amalgamated the concepts of graph theory and metric fixed point theory in a very interesting way and introduced graphical b-metric space as a generalization of b-metric space as follows:…”

Section: Notations Ans Basic Factsmentioning

confidence: 99%

“…In 2017, Shukla et al [24] proposed graphical structure of metric spaces and introduced the notation of graphical metric spaces. Most recently, in 2018, Chuensupantharat et al [7] extended the idea given in [24] and introduced the concept of graphical b-metric spaces along with suitable graphs. On the other side, Reich [23] generalized Banach fixed point theorem for single valued as well as multivalued mappings.…”

Section: Introductionmentioning

confidence: 99%

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Results on contractions of Reich type in graphical b-metric spaces with applications

Younis

Singh

Asadi

et al. 2019

Filomat

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The main purpose of this article is to present some results concerning Reich type contractions in the graph structure in the framework of recently introduced graphical b-metric spaces. Our results are significant extensions and generalizations of some pioneer results in the existing theory. Innovative examples along with directed graphs are propounded to support the newfangled results, making the established theory more comprehensible. Final section is devoted to apply our results to the existence of solutions of some nonlinear problems along with some open problems which may be fruitful for the further scope of the study.

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Section: Discussionmentioning

confidence: 99%

Section: Notations Ans Basic Factsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Results on contractions of Reich type in graphical b-metric spaces with applications

Younis

Singh

Asadi

et al. 2019

Filomat

Self Cite

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“…To avoid repetition, we assume the same terminology, notations, and basic facts as having been utilized in [4]. For more detail, one can also refer to [3,10,11]. In this paper, consider all the graphs are directed unless otherwise stated and Fix(A) denotes the set of fixed points for a mapping A : X → X.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

On Some New Results in Graphical Rectangular b-Metric Spaces

Baradol

Vujaković²,

Gopal

et al. 2020

Mathematics

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In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

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“…Later in 1993, Czerwik [19] provide an axiom that is weaker than the triangular inequality, and formally defined a b-metric space with a sole motive of generalizing the Banach contraction mapping theorem [3]. Subsequently, the concept was improved by many authors [20], others generalized the concept [21,22] and established some fixed point existence results in b-metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Some Globally Stable Fixed Points in b-Metric Spaces

Batsari

Sitthithakerngkiet

2018

Symmetry

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In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete b-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the b-metric function has the regularity property. Our results improve, and generalize some current results in the literature.

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Graphic Contraction Mappings via Graphical b-Metric Spaces with Applications

Cited by 19 publications

References 14 publications

Results on contractions of Reich type in graphical b-metric spaces with applications

Results on contractions of Reich type in graphical b-metric spaces with applications

On Some New Results in Graphical Rectangular b-Metric Spaces

Some Globally Stable Fixed Points in b-Metric Spaces

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