scholarly journals Common Fixed Point Results for Almost ℛg-Geraghty Type Contraction Mappings in b2-Metric Spaces with an Application to Integral Equations

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 101
Author(s):  
Samera M. Saleh ◽  
Salvatore Sessa ◽  
Waleed M. Alfaqih ◽  
Fawzia Shaddad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Binary Relations ◽  
Contraction Mappings ◽  
Partially Ordered ◽  
Linear Integral ◽  
Type Contraction ◽  
Linear Integral Equations

In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of b2-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost g-α-η Geraghty type contraction mappings in b2-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered b2-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.

scholarly journals Some common fixed point theorems for Ciric type contraction mappings

2012 ◽  
Vol 43 (2) ◽  
pp. 187-202
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Type Contraction

Some common fixed point theorems for \'{C}iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3377-3390 ◽  
Author(s):  
Satish Shukla ◽  
Dhananjay Gopal ◽  
Juan Martínez-Moreno
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Complete Metric Spaces ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

scholarly journals Hybrid Multivalued Type Contraction Mappings in αK-Complete Partial b-Metric Spaces and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 86 ◽  
Author(s):  
Eskandar Ameer ◽  
Hassen Aydi ◽  
Muhammad Arshad ◽  
Habes Alsamir ◽  
Mohd Noorani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Nonlinear Matrix ◽  
Set Up ◽  
Type Contraction

In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

scholarly journals Common Fixed Point Results for Set-valued Integral Type Contractions on Metric Spaces with Directed Graph

2020 ◽  
Vol 13 (5) ◽  
pp. 1072-1087
Author(s):  
Saadia Benchabane ◽  
Smail Djebali ◽  
Talat Nazir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Directed Graph ◽  
Metric Spaces ◽  
Integral Type ◽  
Contraction Mappings ◽  
Type Contraction

The aim of this paper is to establish new common fixed pointresults for multivalued integral type contraction mappings on a family of sets endowed with a graph. The obtained results generalize several recent ones. An example of application is included to illustrate the main existence theorem.

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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