Existence of nondecreasing solutions of a quadratic integral equation of Volterra type

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 with a nonlinear perturbation. Banaś et al. [3] proves a few existence theorems for some quadratic integral equations. Banaś and Rzepka [4] study the Volterra quadratic integral equation on unbounded interval. Banaś and Sadarangani [5] study the solvability of Volterra-Stieltjes integral equation. In [6-8] the authors proved the existence of nondecreasing solutions of a quadratic integral equation. Dhage [9-10] proves an existence theorem for a certain differential inclusions in Banach algebras. Dhage [11] proves the existence results of some nonlinear functional integral equations. The purpose of this paper is to continue the study of those authors. Using the theory of measures of noncompactness and applying a new method, we prove the existence results of quadratic integral equations of Volterra type.