Abstract
AbstractThe aim of the present paper is to introduce a new family of measures of noncompactness on the Frechet space LPloc(ℝN) (1 ≤ p < ∞). Further, we prove a fixed point theorem on the family of ...
Highlights
Introduction and preliminariesThe concept of a measure of noncompactness (MNC) plays a signification role in the nonlinear functional analysis
Metric fixed point theory is a powerful tool for solving several problems in various parts of mathematics and its applications
We introduce a new family of measures of noncompactness in the Frechet space lploc(RN) and by applying this family of measures of noncompactness, we discuss the existence of solutions for some classes of nonlinear functional integral equations
Summary
Metric fixed point theory is a powerful tool for solving several problems in various parts of mathematics and its applications. Olszowy introduced a new family of measures of noncompactness on the space L1locðRþÞ consisting of all real functions locally integrable on Rþ, equipped with a suitable topology. She studied the existence of solutions of a nonlinear Volterra integral equation in the space L1locðRþÞ (cf Olszowy, 2014). By using an extension of Darbo’s fixed point theorem associated with this new family of measures of noncompactness. (Tychonoff fixed point theorem Agarwal, Meehan, & O’Regan, 2001) Let E be a Hausdorff locally convex linear topological space, C a nonempty convex subset of E and F : C !
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