Address: Department of Mathematics and Statistics, Faculty of Science, Mu’tah University, P.O. Box (7), Al-Karak, Jordan
E-mail: malik_okasha@yahoo.com
Abstract: The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.
AMSclassification: primary 54H25; secondary 47H05, 47H09, 47H10.
Keywords: fuzzy metric space, t-norm of h-type, topological degree theory.
DOI: 10.5817/AM2019-2-83