Weak solutions of a functional integral equation in reflexive Banach space

2016 ◽  
Vol 4 ◽  
pp. 305-313 ◽  
Author(s):  
Ahmed M. A. El-Sayed ◽  
Nesreen F. M. El-haddad
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Weak Solutions ◽  
Reflexive Banach Space ◽  
Functional Integral

scholarly journals Weak Solutions of a Coupled System of Urysohn-Stieltjes Functional (Delayed) Integral Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
M. M. A. Al-Fadel
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Weak Solutions ◽  
Reflexive Banach Space ◽  
Coupled System ◽  
Functional Integral ◽  
Existence Of Weak Solutions ◽  
Functional Integral Equations ◽  
Stieltjes Type

We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach spaceE. As an application, the coupled system of Hammerstien-Stieltjes functional integral equations is also studied.

scholarly journals On the Weak Solutions of a Delay Composite Functional Integral Equation of Volterra-Stieltjes Type in Reflexive Banach Space

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 245
Author(s):  
Ahmed M. A. El-Sayed ◽  
Yasmin M. Y. Omar
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Continuous Dependence ◽  
Reflexive Banach Space ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Reflexive Banach Spaces ◽  
Delay Function ◽  
Stieltjes Type ◽  
Differential And Integral Equations

Differential and integral equations in reflexive Banach spaces have gained great attention and hve been investigated in many studies and monographs. Inspired by those, we study the existence of the solution to a delay functional integral equation of Volterra-Stieltjes type and its corresponding delay-functional integro-differential equation in reflexive Banach space E. Sufficient conditions for the uniqueness of the solutions are given. The continuous dependence of the solutions on the delay function, the initial data, and some others parameters are proved.

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 Solvability of functional-integral equations (fractional order) using measure of noncompactness

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

scholarly journals On the functional-integral equation of Volterra type with weakly singular kernel

2008 ◽  
Vol 83 (97) ◽  
pp. 57-63
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Singular Kernel ◽  
Volterra Type ◽  
Weakly Singular Kernel ◽  
Measures Of Noncompactness ◽  
Weakly Singular

We give sufficient conditions for the existence of Lp-solution of a Volterra functional-integral equation in a Banach space. Our assumptions and proofs are expressed in terms of measures of noncompactness.

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