scholarly journals Kannan-Type Contractions on New Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hassen Aydi ◽  
Muhammad Aslam ◽  
Dur-e-Shehwar Sagheer ◽  
Samina Batul ◽  
Rashid Ali ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Asymptotic Regularity ◽  
Existence Of A Solution ◽  
Fredholm Type ◽  
Type Integral

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.

scholarly journals Common Fixed Points Technique for Existence of a Solution of Urysohn Type Integral Equations System in Complex Valued b-Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 400
Author(s):  
Muhammad Suhail Aslam ◽  
Monica Felicia Bota ◽  
Mohammad S. R. Chowdhury ◽  
Liliana Guran ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Existence Of A Solution ◽  
Contraction Condition ◽  
Type Integral ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given.

scholarly journals Fixed points of $(\psi, \phi)-$contractions and Fredholm type integral equation

2021 ◽  
Vol 2 (1) ◽  
pp. 91-100
Author(s):  
Nabil Mlaiki ◽  
Doaa Rizk ◽  
Fatima Azmi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Contractive Mappings ◽  
Type Integral

In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces for mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, we give an application of our results as an integral equation.

scholarly journals Fixed Points of Set-valued F-contraction Operators in Quasi-ordered Metric Spaces with an Application to Integral Equations

2021 ◽  
pp. 152-160
Author(s):  
Ehsan Lotfali Ghasab ◽  
Hamid Majani ◽  
Ghasem Soleimani Rad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Ordered Metric Spaces ◽  
Banach Contraction ◽  
Type Integral

In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since we present Banach contraction principle in a different manner from that which is known in the present literature. Some examples and an application to existence of solution of Volterra-type integral equation are given to support the obtained results

scholarly journals On some fixed point theorems for multivalued F-contractions in partial metric spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 151-161
Author(s):  
Santosh Kumar ◽  
Sholastica Luambano
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces

Abstract Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.

scholarly journals New Fixed Point Results via (q,y)R-Weak Contractions with an Application

2020 ◽  
Author(s):  
Mohammad Imded ◽  
Based Ali ◽  
Waleed M. Alfaqih ◽  
Salvatore Sessa
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Auxiliary Functions ◽  
Type Integral

In this paper, inspired by Jleli and Samet [journal of inequalities and applications 38 (2014) 2 1–8] we introduce two new classes of auxiliary functions and utilize the same to define (q, y)R-weak 3 contractions. Utilizing (q, y)R-weak contractions, we prove some fixed point theorems in the setting 4 of relational metric spaces. We employ some examples to substantiate the utility of our newly proved 5 results. Finally, we apply one of our newly proved results to ensure the existence and uniqueness of 6 solution of a Volterra-type integral equation.

scholarly journals Ordered-Theoretic Fixed Point Results in Fuzzy b-Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalil Javed ◽  
Fahim Uddin ◽  
Hassen Aydi ◽  
Aiman Mukheimer ◽  
Muhammad Arshad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fredholm Type ◽  
Banach Contraction ◽  
Type Integral

The aim of this manuscript is to initiate the study of the Banach contraction in R-fuzzy b-metric spaces and discuss some related fixed point results to ensure the existence and uniqueness of a fixed point. A nontrivial example is imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the provided results, an application is presented to solve the first kind of a Fredholm-type integral equation.

scholarly journals New Fixed Point Results via (θ,ψ)R-Weak Contractions with an Application

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 887
Author(s):  
Mohammad Imdad ◽  
Based Ali ◽  
Waleed M. Alfaqih ◽  
Salvatore Sessa ◽  
Abdullah Aldurayhim
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Auxiliary Functions ◽  
Type Integral ◽  
Uniqueness Of The Solution

In this paper, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1–8), we introduce two new classes of auxiliary functions and utilize the same to define ( θ , ψ ) R -weak contractions. Utilizing ( θ , ψ ) R -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation.

scholarly journals New Fixed Point Results in F-Quasi-Metric Spaces and an Application

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ehsan Lotfali Ghasab ◽  
Hamid Majani ◽  
Erdal Karapinar ◽  
Ghasem Soleimani Rad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Volterra Type ◽  
Type Integral ◽  
The Given

The main goal of the present paper is to obtain several fixed point theorems in the framework of F-quasi-metric spaces, which is an extension of F-metric spaces. Also, a Hausdorff δ-distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type integral equation.

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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