scholarly journals Solving a Class of Integral Equations via Contractive Mapping with Rational Type

2020 ◽  
Vol 13 (4) ◽  
pp. 995-1015
Author(s):  
Abdullah Abdullah ◽  
Muhammad Sarwar ◽  
Zead Mustafa ◽  
Mohammed M.M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Coupled Fixed Point Theorem ◽  
Set Up ◽  
Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

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 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.

On a generalized coupled fixed point theorem in C[0, 1] and its application to a class of coupled systems of functional-integral equations

2015 ◽  
Vol 31 (3) ◽  
pp. 333-337
Author(s):  
J. HARJANI ◽  
◽  
J. ROCHA ◽  
K. SADARANGANI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Coupled Fixed Point ◽  
General System ◽  
Functional Integral ◽  
Coupled Systems ◽  
Nonlinear Functional ◽  
Coupled Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0, 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0, 1] for a general system of nonlinear functional-integral equations with maximum.

scholarly journals Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Hassen Aydi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Coupled Fixed Point Theorem ◽  
Partial Metric Spaces ◽  
Ordered Partial Metric Space ◽  
Coupled Fixed Points

In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappingsF:X×X→Xandg:X→Xon a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012).

scholarly journals Modified F-contractions via α-admissible mappings and application to integral equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1141-1148 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapinar ◽  
Habib Yazidi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces

In this paper, we introduce the concept of a modified F-contraction via ?-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.

scholarly journals An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 879-886 ◽  
Author(s):  
A. Samadi ◽  
M.B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point ◽  
Coupled Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

In this paper, an extension of Darbo fixed point theorem is introduced. By applying our extension, we obtain a coupled fixed point theorem and a solution for an integral equation. The proofs of our results are based on the technique of measure of noncompactness.

scholarly journals Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces

2020 ◽  
pp. 492-502 ◽  
Author(s):  
Rao, N. Seshagiri ◽  
Karusala Kalyani
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Mixed Monotone Property ◽  
Ordered Metric Spaces ◽  
Rational Type

The purpose of this paper is to establish some coupled fixed point theorems for a self mapping satisfying certain rational type contractions along with strict mixed monotone property in a metric space endowed with partial order. Also, we have given the result of existence and uniqueness of a coupled fixed point for the mapping. This result generalize and extend several well known results in the literature

scholarly journals Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdullah Shoaib ◽  
Qasim Mahmood ◽  
Aqeel Shahzad ◽  
Mohd Salmi Md Noorani ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Rational Contraction ◽  
Rational Type

AbstractThe objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

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