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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.

Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

Abbas S., Agarwal R. P., Benchohra M., Berhoun F.

Demonstratio Mathematica

2018

Vol. 51, nr 1

131--140

In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

On the Existence and Local Asymptotic Stability of Solutions of Fractional Order Integral Equations

Abbas S., Benchohra M.

Commentationes Mathematicae

2012

Vol. 52, [Z] 1

91-100

In this paper, we present some results concerning the existence and the local asymptotic stability of solutions for a functional integral equation of fractional order, by using some fixed point theorems.

On the Existence of Solutions of Some Stochastic Functional Integral Equations

Pasławska-Południak M.

Commentationes Mathematicae

2010

Vol. 50, [Z] 1

49-60

The integral equation of Urysohn type is considered, for the deterministic and stochastic cases . We show, using the fixed point theorem of Darbo type that under some assumptions the equations have solutions belonging to the space of continuous functions. The main tool used in our paper is the technique associated with measures of noncompactness.