scholarly journals Some Results on N-Tupled Coincidence and Fixed Points of Graphs on Metric Spaces and an Application to Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Ahmed H. Soliman ◽  
Tamer Nabil
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Systems Of Integral Equations ◽  
Theoretical Results

In this work, we establish some N-tupled common coincidence and N-tupled common fixed points for the mappings satisfying a (φ-ψ)-type contractive condition in a complete metric space endowed with a directed graph (for short digraph). Also, we apply our theoretical results to study the existence and uniqueness of solutions for systems of integral equations.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals Common fixed point theorems for asymptotically regular mappings on ordered orbitally complete metric spaces with an application to systems of integral equations

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3277-3289
Author(s):  
Hemant Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equations ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Systems Of Integral Equations ◽  
Weakly Increasing Maps ◽  
Asymptotically Regular

In this paper, we prove existence and uniqueness results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces under generalized ?-contractive condition. Also, we introduce and use orbitally dominating maps and orbitally weakly increasing maps. We furnish suitable examples to demonstrate the usability of the hypotheses of our results. As an application, we prove the existence of solutions for certain system of integral equations.

scholarly journals A New Class of Contraction inb-Metric Spaces and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Preeti Kaushik ◽  
Sanjay Kumar ◽  
Kenan Tas
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
New Class ◽  
End Results

A novel class ofα-β-contraction for a pair of mappings is introduced in the setting ofb-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.

scholarly journals Common Fixed Points for Nonlinear Quasi-Contractions of Ćirić Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Positive Answer ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Scalarization Method ◽  
Cone Metric

We establish common fixed points theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type with aQ-function. Furthermore, using the scalarization method, we deduce some results of common fixed point in tvs-cone metric spaces with ac-distance. As application, we give a positive answer to the question of Ćirić et al. posed in 2012. Our results extend and generalize many recent results.

scholarly journals Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg ◽  
Poom Kumam
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Implicit Relation ◽  
Existence And Uniqueness Results ◽  
Contractive Mappings ◽  
Uniqueness Results ◽  
Relation Type

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals Common Fixed Points for Weakψ-Contractive Mappings in Ordered Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sumit Chandok ◽  
Simona Dinu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

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