scholarly journals Analytical Solution for Differential and Nonlinear Integral Equations via F ϖ e -Suzuki Contractions in Modified ϖ e -Metric-Like Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Nonlinear Integral Equations ◽  
New Space

The aim of this manuscript is to present a new space, namely, a modified ϖ e -metric-like space, and we establish some related fixed point results using extended F ϖ e -Suzuki and generalized F ϖ e -Suzuki contractions on the mentioned space. Here, we support our theoretical consequences in two ways: the first one consists of presenting illustrative examples and the second one consists of finding analytical solutions for some integral and differential equations in the context of the mentioned space.

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 Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

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.

scholarly journals Fixed Point Theorems for ${\mathscr{Z}}_{\vartheta}$ -Contraction and Applications to Nonlinear Integral Equations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 120023-120029
Author(s):  
Xiangling Li ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Ekrem Savas
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equations

scholarly journals On theRF-pair operations for the exact solution of some classes of nonlinear Volterra integral equations

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
P. Darania ◽  
M. Hadizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Original Equation ◽  
Nonlinear Integral Equations ◽  
Integrable Equations

We study the exact solution of some classes of nonlinear integral equations by series of some invertible transformations andRF-pair operations. We show that this method applies to several classes of nonlinear Volterra integral equations as well and give some useful invertible transformations for converting these equations into differential equations of Emden-Fowler type. As a consequence, we analyze the effect of the proposed operations on the exact solution of the transformed equation in order to find the exact solution of the original equation. Some applications of the method are also given. This approach is effective to find a great number of new integrable equations, which thus far, could not be integrated using the classical methods.

Sign in / Sign up

Export Citation Format

Share Document