scholarly journals On Fixed Point Results in Gb-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 617 ◽  
Author(s):  
Hassen Aydi ◽  
Dušan Rakić ◽  
Asadolah Aghajani ◽  
Tatjana Došenović ◽  
Mohd Salmi Md Noorani ◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Partially Ordered ◽  
Tripled Coincidence Point ◽  
Contractive Mappings

The purpose of this paper is to consider various results in the context of G b -metric spaces that have been recently published after the paper (Aghajani, A.; Abbas, M.; Roshan, J.R. Common fixed point of generalized weak contractive mappings in partially ordered G b -metric spaces. Filomat 2014, 28, 1087–1101). Our new results improve, complement, unify, enrich and generalize already well known results on G b -metric spaces. Moreover, some coupled and tripled coincidence point results have been provided.

scholarly journals Some fixed point results of generalized $$(\phi , \psi )$$-contractive mappings in ordered b-metric spaces

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Belay Mitiku ◽  
Kalyani Karusala ◽  
Seshagiri Rao Namana
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Common Fixed Points ◽  
Coupled Coincidence Point ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract Objectives The aim of this paper is to establish some fixed point, coincidence point and, coupled coincidence and coupled common fixed point results for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in partially ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify our results. Result The existence and uniqueness theorems for a fixed point and coincidence point, coupled coincidence point and coupled common fixed points for two mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.

scholarly journals Tripled Coincidence Point Results for $(\psi,\varphi)$-weakly Contractive Mappings in Partially Ordered S-matric Spaces

2017 ◽  
Vol 9 (5) ◽  
pp. 108
Author(s):  
Abdolsattar Gholidahneh ◽  
Shaban Sedghi
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Monotone Mappings ◽  
Partially Ordered ◽  
Tripled Coincidence Point ◽  
Contractive Mappings ◽  
Weakly Contractive

In this paper, the notion of $ S $-metric spaces will be introduced. We present a some tripled coincidence point results for a mixed $ g $-monotone mappings $ F : X^{3} \rightarrow X $ satisfying $ (\psi,\varphi) $-contractions in partially ordered complete $ S $-metric spaces. Also an application and some example are given to support our results.

scholarly journals Generalized Contractive Mappings and Weaklyα-Admissible Pairs inG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
N. Hussain ◽  
V. Parvaneh ◽  
S. J. Hoseini Ghoncheh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Periodic Points ◽  
Contractive Mappings ◽  
Admissible Pairs ◽  
Weakly Contractive ◽  
Common Fixed Point Theorems

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ,φ)-contractive mappings using partially weaklyG-α-admissibility in the setup ofG-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially orderedG-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

scholarly journals Common Fixed Point of (ψ, β)-Generalized Contractive Mappings in Partially Ordered Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Abbas ◽  
I. Zulfaqar ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings

Gordji et al. (2012) gave a generalization of Geraghty’s theorem. The aim of this paper is to study the necessary conditions for the existence of coincidence and common fixed point of four mappings satisfying (ψ, β)-generalized contractive condition in the setup of partial ordered metric spaces. Some examples are given to validate the definitions and results presented herein.

scholarly journals Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1087-1101 ◽  
Author(s):  
Asadollah Aghajani ◽  
Mujahid Abbas ◽  
Jamal Roshan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Weakly Compatible ◽  
Compatible Condition ◽  
New Type ◽  
Common Fixed Point Theorem

In this work, using the concepts of G-metric and b-metric we define a new type of metric which we call Gb-metric. We study some basic properties of such metric. We also prove a common fixed point theorem for six mappings satisfying weakly compatible condition in complete partially ordered Gb-metric spaces. A nontrivial example is presented to verify the effectiveness and applicability of our main result.

scholarly journals Coupled and Tripled Coincidence Point Results with Application to Fredholm Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Nawab Hussain ◽  
Jamal Rezaei Roshan ◽  
Vahid Parvaneh
Keyword(s):  
Integral Equations ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fredholm Integral Equations ◽  
Partially Ordered ◽  
Tripled Coincidence Point ◽  
Contractive Mappings ◽  
Nonlinear Fredholm Integral Equations

The aim of this paper is to define weakα-ψ-φ-contractive mappings and to establish coupled and tripled coincidence point theorems for such mappings defined onGb-metric spaces using the concept of rectangularG-α-admissibility. As an application, we derive new coupled and tripled coincidence point results for weakψ-φ-contractive mappings in partially orderedGb-metric spaces. Our results are generalizations and extensions of some recent results in the literature. We also present an example as well as an application to nonlinear Fredholm integral equations in order to illustrate the effectiveness of our results.

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Asadollah Aghajani ◽  
Mujahid Abbas ◽  
Jamal Roshan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Partially Ordered ◽  
Contractive Mappings

AbstractWe prove some common fixed point results for four mappings satisfying generalized weak contractive condition in partially ordered complete b-metric spaces. Our results extend and improve several comparable results in the existing literature

scholarly journals Tripled and coincidence fixed point theorems for contractive mappings satisfying Φ-maps in partially ordered metric spaces

2014 ◽  
Vol 22 (3) ◽  
pp. 179-204 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Mihai Postolache ◽  
Zead Mustafa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Nonlinear Contraction ◽  
Coincidence Fixed Point

Abstract In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and ɡ : X → X satisfying a nonlinear contraction based on ϕ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results.

scholarly journals On Generalized WeaklyG-Contractive Mappings in Partially OrderedG-Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
A. Razani ◽  
V. Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Periodic Points ◽  
Partially Ordered ◽  
Contractive Mappings

The aim of this paper is to present some coincidence and common fixed point results for generalized weaklyG-contractive mappings in the setup of partially orderedG-metric space. We also provide an example to illustrate the results presented herein. As an application of our results, periodic points of weaklyG-contractive mappings are obtained.

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