On Erdélyi–Kober Quadratic Functional-Integral Equation in Banach Algebra

2017 ◽  
Vol 39 (3) ◽  
pp. 276-294 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Bessem Samet
Keyword(s):  
Integral Equation ◽  
Banach Algebra ◽  
Functional Integral ◽  
Quadratic Functional

Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Ahmed El-Sayed ◽  
Hind Hashem
Keyword(s):  
Integral Equation ◽  
Banach Algebra ◽  
Existence Theorem ◽  
Fractional Order ◽  
Continuous Solution ◽  
Functional Integral ◽  
Existence Results ◽  
Quadratic Functional ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractWe present an existence theorem for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional order. Also, a general quadratic integral of fractional order will be considered.

scholarly journals Asymptotically Stable Solutions of a Generalized Fractional Quadratic Functional-Integral Equation of Erdélyi-Kober Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Beata Rzepka
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Stable Solution ◽  
Functional Integral ◽  
Quadratic Functional ◽  
Asymptotically Stable ◽  
Stable Solutions ◽  
Asymptotically Stable Solution

We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach spaceBC(ℝ+). We show that this equation has at least one asymptotically stable solution.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

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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