We consider a very general quadratic integral equation and we prove the existence of monotonic solutions of this equation in C[0,1]. Our analysis depends on a suitable combination of the measure of noncompactness introduced by Banaś and Olszowy and the Darabo fixed point theorem.

In this paper we prove theorems on the existence of integrable and monotonic solutions of nonlinear integral equation in Lebesgue Space. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to the so-called measure of weak noncompactness.

We give a survey of the known results concerning the sets c0(Λ), c(Λ) and c∞(Λ) including their basic topological properties, their first and second dual spaces, and the characterizations of matrix transformations from them into the spaces l∞, c and c0. Furthermore, we establish some new results such as the representations of the general bounded linear operators from c(Λ) into the spaces l∞, c ...

In this paper we prove existence theorems for integro – differential equations x(t) = f(t, x(t), ∫ t 0 k(t, s, x(s))∆s), x(0) = x0 t ∈ Ia = [0, a] ∩ T, a ∈ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil d...

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

Abstract The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations finite delay. arguments are based on a fixed point theorem stochastic domain combined measure noncompactness. An illustration is given to show applicability our results.