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 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 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 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.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals Coincidence and common fixed point theorems for four mappings satisfying (αs, F)-contraction

2018 ◽  
Vol 23 (5) ◽  
pp. 664-690 ◽  
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Common Solution ◽  
Type Integral ◽  
Common Fixed Point Theorems

In this paper, we manifest some coincidence and common fixed point theorems for four self-mappings satisfying Círíc-type and Hardy–Rogers-type (αs,F)-contractions defined on an αs-complete b-metric space. We apply these results to infer several new and old corresponding results in ordered b-metric spaces and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We present examples to validate our results. We discuss an application of main result to show the existence of common solution of the system of Volterra type integral equations.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

scholarly journals Fixed Point Results for a New Class of Multi-Valued Mappings Under (θ; R)-Contractions With an Application

2020 ◽  
Author(s):  
MD Hasanuzzaman Hasanuzzaman ◽  
Salvatore Sessa ◽  
Mohammad Imdad ◽  
W. M. Alfaqih
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solution ◽  
Binary Relation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Volterra Type ◽  
New Class

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

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.

Sign in / Sign up

Export Citation Format

Share Document