A Family of Measures of Noncompactness in the Space L1loc (ℝ+) Lloc1(R+) and its Application to Some Nonlinear Volterra Integral Equation

Abstract

The aim of this paper is to study a new family of measures of noncompactness in the space L1loc (ℝ+) consisting of all real functions locally integrable on ℝ+, equipped with a suitable topology. As an example of applications of the technique associated with that family of measures of noncompactness, we study the existence of solutions of a nonlinear Volterra integral equation in the space L1loc (ℝ+). The obtained result generalizes several ones obtained earlier with help of other methods. © 2013 The Author(s).