A family of measures of noncompactness in the space Lploc(ℝN) and its application to some nonlinear convolution type integral equations. Issue 1 (1st January 2019)

• Record Type: Journal Article
• Authors: Amiri Kayvanloo, Hojjatollah; Khanehgir, Mahnaz; Allahyari, Reza
• Editors: Srivastava, Hari M.
• Is Part Of: Cogent mathematics & statistics. Volume 6:Issue 1(2019)
• Publication Date: 2019-01-01
• Subjects: Darbo's fixed point theorem -- Family of measures of noncompactness -- Fixed point -- Integral equations; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/25742558.2019.1592276
• Languages: English
• ISSNs: 2574-2558

Abstract

Abstract: The aim of the present paper is to introduce a new family of measures of noncompactness on the Fr é chet space L P loc (ℝ N ) (1 ≤ p < ∞). Further, we prove a fixed point theorem on the family of measures of noncompactness in L P loc (ℝ N ). As an application, we investigate the existence of entire solutions for some classes of nonlinear functional integral equations of convolution type associated with the new family of measures of noncompactness. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.