scholarly journals Some Common Fixed Point Theorems for Generalized F-Contraction Involving w-Distance with Some Applications to Differential Equations

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 32
Author(s):  
Chirasak Mongkolkeha ◽  
Dhananjay Gopal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Second Order Differential Equation ◽  
Common Fixed Point Theorems

In this paper, we introduce the Ćirić type generalized F-contraction and establish certain common fixed point results for such F-contraction in metric spaces with the w-distances. In addition, we give some examples to support our results. Finally, we apply our results to show the existence of solutions of the second order differential equation.

scholarly journals New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 324 ◽  
Author(s):  
Sujitra Sanhan ◽  
Winate Sanhan ◽  
Chirasak Mongkolkeha
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Generalized Pseudodistance

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

scholarly journals Some Coincidence and Common Fixed Point Results in Fuzzy Metric Space with an Application to Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Iqra Shamas ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fuzzy Metric ◽  
Weak Compatibility ◽  
Common Fixed Point Theorems

In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work.

scholarly journals Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sunny Chauhan ◽  
Mohammad Imdad ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

scholarly journals Common Fixed Point Results for Generalized g − α s p , ψ , φ Contractive Mappings with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jianju Li ◽  
Hongyan Guan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
New Class ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

In this paper, we introduce a new class of g − α s p − admissible mappings and prove some common fixed point theorems involving this new class of mappings which satisfy generalized contractive conditions in the framework of b − metric spaces. We also provide two examples to show the applicability and validity of our results. Meanwhile, we present an application to the existence of solutions to an integral equation by means of one of our results.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

scholarly journals Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

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