In this brief note,  using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove  an existence result for a quadratic  integral equation of Hammerstein type on an unbounded interval in two variables  which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...

Abstract In this work, we study the existence of one and exactly solution x ? C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation Volterra-Stieltjes type. As special cases fractional order Ch...

where f, g : I × → are given functions, λ ∈ (0, 1]. The study of quadratic integral equation has received much attention over the last thirty years or so. For instance, Cahlon and Eskin [1] prove the existence of positive solutions in the space C[0, 1] and Cα[0, 1] of an integral equation of the Chandrasekhar H-equation with perturbation. Argyros [2] investigates a class of quadratic equations ...

In this article, we investigate the analytical and approximate solutions for a fractional quadratic integral equation in frame of generalized Riemann–Liouville operator with respect to another function. The existence uniqueness results obtained. Moreover, some new special corresponding suitable values parameters ζ q are given. main proved by applying Banach’s fixed point theorem, Adomian decomp...

We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of mea...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in IR. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic control problem, which leads to the feedback form of the optimal control. This is in contrast with previous papers on the subject, which confine themselves to study the F...