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

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.

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3234
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hind H. G. Hashem ◽  
Shorouk M. Al-Issa

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.


Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
M. M. A. Al-Fadel

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.


2008 ◽  
Vol 83 (97) ◽  
pp. 57-63
Author(s):  
Aldona Dutkiewicz

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.


CAUCHY ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 167
Author(s):  
Minanur Rohman

<p class="AbstractCxSpFirst">In this paper, we will discuss some applications of almost surjective epsilon-isometry mapping, one of them is in Lorentz space ( L_(p,q)-space). Furthermore, using some classical theorems of w star-topology and concept of closed subspace -complemented, for every almost surjective epsilon-isometry mapping  <em>f </em>: <em>X to</em><em> Y</em>, where <em>Y</em> is a reflexive Banach space, then there exists a bounded linear operator   <em>T</em> : <em>Y to</em><em> X</em>  with  such that</p><p class="AbstractCxSpMiddle">  </p><p class="AbstractCxSpLast">for every x in X.</p>


2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Beata Rzepka

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.


2004 ◽  
Vol 2004 (9) ◽  
pp. 469-478 ◽  
Author(s):  
D. Bahuguna ◽  
Reeta Shukla

We consider a class of quasilinear integrodifferential equations in a reflexive Banach space. We apply the method of semidiscretization in time to establish the existence, uniqueness, and continuous dependence on the initial data of strong solutions.


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