Nondecreasing solutions of a quadratic integral equation of Urysohn type

Abstract

Applying the technique associated with measures of noncompactness, we prove the existence of nondecreasing solutions of a quadratic integral equation of Urysohn type in the space of real functions defined and continuous on a closed hounded interval. (~)

Solvability of Chandrasekhar’s Quadratic Integral Equations in Banach Algebra

“…Functional integral and differential equations of different types play an im-portant and a fascinating role in nonlinear analysis and finding various ap-plications in describing of several real world problems [2] [3] [4] [5] [6] [7] [8] [9].…”

A mixed Hammerstein integral equation

“…In [11], J.Banas , J. Caballero, J.Rocha, and K. Sadaragani established the existence of nondecreasing continuous solutions on a bounded and closed interval I to the nonlinear integral equation of Volterra type f (x) = a(x) + (T f )(x) x 0 v(x, y, f (y))dy, y ∈ I, under a set of conditions on the functions a, v, and on the continuous operator T : C(I) → C(I). A similar result is presented by W.G.El-Sayed and B.Rzepka in [12] for the quadratic integral equation of Urysohn type with the form f (x) = a(x) + H(x, f (x)) 1 0 u(x, y, f (y))dy, y ∈ I. Due to plenty of practical applications, numerical methods for solving integral equations are of great interest.…”

Some generalizations of Darbo fixed point theorem and its application

“…(1.1) generates the superposition operator H defined by the formula .H x/.t / D h.t; x.t // where x D x.t / is an arbitrary function defined on I (cf. [7], [11]). We show that Eq.…”