Coupled fixed point results for nonlinear integral equations

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

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Common coupled fixed point results for operators without mixed monotone type properties and application to nonlinear integral equations

Fixed Point Theory and Applications ◽

10.1186/s13663-017-0595-y ◽

2016 ◽

Vol 2017 (1) ◽

Author(s):

Nabil Machrafi

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Coupled Fixed Point ◽

Nonlinear Integral Equations ◽

Common Coupled Fixed Point ◽

Monotone Type

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A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

Mathematics ◽

10.3390/math7070634 ◽

2019 ◽

Vol 7 (7) ◽

pp. 634 ◽

Cited By ~ 6

Author(s):

Hasanen Abuelmagd Hammad ◽

Manuel De la De la Sen

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Contraction Mapping ◽

Complete Metric Space ◽

Coupled Fixed Point ◽

Coupled Systems ◽

Uniqueness Of Solutions ◽

Nonlinear Integral Equations ◽

Contraction Condition ◽

Fixed Point Technique

In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed.

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Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

Advances in Difference Equations ◽

10.1186/s13662-020-03132-8 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Gui-Xiu Chen ◽

Shamoona Jabeen ◽

Saif Ur Rehman ◽

Ahmed Mostafa Khalil ◽

Fatima Abbas ◽

...

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Coupled Fixed Point ◽

Nonlinear Integral Equations ◽

Cone Metric Spaces ◽

Contraction Mappings ◽

Point Analysis ◽

Cone Metric

AbstractIn this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

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Coupled fixed point theorems for contractive mappings involving new function classes and applications

Filomat ◽

10.2298/fil1707893a ◽

2017 ◽

Vol 31 (7) ◽

pp. 1893-1907 ◽

Cited By ~ 5

Author(s):

Arslan Ansari ◽

Hüseyin Işik ◽

Stojan Radenovic

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Coupled Fixed Point ◽

Nonlinear Integral Equations ◽

Existence Of A Solution ◽

Ordered Metric Spaces ◽

Contractive Mappings ◽

Function Classes

The aim of this paper is to introduce the notions of ?-(F,H)-(?,?) and ?-(F,H)-(?,?) contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

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

Advances in Difference Equations ◽

10.1186/s13662-021-03458-x ◽

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).

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An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

Advances in Difference Equations ◽

10.1186/s13662-020-02936-y ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Amar Deep ◽

Deepmala ◽

Jamal Rezaei Roshan ◽

Kottakkaran Sooppy Nisar ◽

Thabet Abdeljawad

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Integral Equations ◽

Point Theorem ◽

Measure Of Noncompactness ◽

Existence Results ◽

Nonlinear Integral Equations ◽

Existence Of A Solution ◽

Darbo’S Fixed Point Theorem ◽

Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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