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On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

Metwali Mohamed M. A.

Demonstratio Mathematica

2020

Vol. 53, nr 1

86--94

The existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.

Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

Rehman Habib ur, Gopal Dhananjay, Kumam Poom

Demonstratio Mathematica

2019

Vol. 52, nr 1

166--182

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α-ψ and β-ψ con-densing operators and using them we propose new fixed point results. Our results generalize and extendsome comparable results from the literature. Additionally, as an application, we apply the obtained fixedpoint theorems to study the nonlinear functional integral equations.

On a cubic integral equation of Urysohn type with linear perturbation of second kind

Awad H. K., Darwish M. A., Metwali M. M. A.

Journal of Mathematics and Applications

2018

Vol. 41

29--38

In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.