scholarly journals On Chandrasekhar functional integral inclusion and Chandrasekhar quadratic integral equation via a nonlinear Urysohn–Stieltjes functional integral inclusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed ◽  
Shorouk Al-Issa ◽  
Yasmin Omar
Keyword(s):  
Integral Equation ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Integral Inclusion ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Stieltjes Type

AbstractWe investigate the existence of solutions for a nonlinear integral inclusion of Urysohn–Stieltjes type. As applications, we give a Chandrasekhar quadratic integral equation and a nonlinear Chandrasekhar integral inclusion.

scholarly journals On the Existence of the Solutions of a Fredholm Integral Equation with a Modified Argument in Hölder Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 522 ◽  
Author(s):  
Merve Temizer Ersoy ◽  
Hasan Furkan
Keyword(s):  
Integral Equation ◽  
Existence Of Solutions ◽  
Hölder Spaces ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Conclusion Section ◽  
The Given ◽  
Holder Spaces

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, x ( t ) = p ( t ) + x ( t ) ∫ 0 1 k ( t , τ ) ( T x ) ( τ ) d τ , where p , k are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted.

scholarly journals Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation

2021 ◽  
Vol 54 (1) ◽  
pp. 25-36
Author(s):  
Ahmed M. A. El-Sayed ◽  
Yasmin M. Y. Omar
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fractional Order ◽  
Special Cases ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Stieltjes Type

Abstract In this work, we study the existence of one and exactly one solution x ∈ C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.

On a nonlinear quadratic integral equation of Urysohn–Stieltjes type and its applications

2001 ◽  
Vol 47 (2) ◽  
pp. 1175-1186 ◽  
Author(s):  
Józef Banaś ◽  
Juan Ramon Rodriquez ◽  
Kishin Sadarangani
Keyword(s):  
Integral Equation ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Stieltjes Type

scholarly journals Solvability of a Quadratic Integral Equation of Fredholm Type with Supremum in Hölder Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
J. Caballero Mena ◽  
R. Nalepa ◽  
K. Sadarangani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Holder Spaces

Using the classical Schauder fixed point theorem, we prove the existence of solutions of a quadratic integral equation of Fredholm type with supremum in the space of functions satisfying the Hölder condition.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral

2017 ◽  
Vol 9 (5) ◽  
pp. 46
Author(s):  
Hui Mei ◽  
Guoju Ye ◽  
Wei Liu ◽  
Yanrong Chen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Stieltjes Integral

In this paper, we apply the method associated with the technique of measure of noncompactness and some generalizations of Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile, an example is provided to illustrate our results.

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