Generalized fractals in semimetric spaces. (July 2022)

• Record Type: Journal Article
• Authors: Bessenyei, Mihály; Pénzes, Evelin
• Is Part Of: Nonlinear analysis. Volume 220(2022)
• Publication Date: 2022-07
• Subjects: primary 47H09 -- secondary 47H10 28A80; Semimetric space -- Fractal -- Kuratowski noncompactness -- Hausdorff–Pompeiu distance -- Hausdorff dimension -- Fixed point theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112853
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of the present paper is to extend the classical fractal theory using condensing maps and generalized contractions of semimetric spaces. Our method is independent from the approach of Hutchinson: It is based on the Kuratowski measure of noncompactness and avoids completely the Blaschke Completeness Theorem.