scholarly journals Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Shagun Sharma ◽  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Contraction Mappings

Using the idea of modified ϱ -proximal admissible mappings, we derive some new best proximity point results for ϱ − ϑ -contraction mappings in metric spaces. We also provide some illustrations to back up our work. As a result of our findings, several fixed-point results for such mappings are also found. We obtain the existence of a solution for nonlinear integral equations as an application.

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

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.

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

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1893-1907 ◽  
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.

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

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.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

scholarly journals Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Choonkil Park ◽  
Manuel de la Sen ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
New Type ◽  
Uniqueness And Existence

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

Sign in / Sign up

Export Citation Format

Share Document