Some Properties Of Cartesian Product Of Two Fuzzy Normed Spaces (Journal of the College of Basic Education, 2023)
In this paper , the concept of the Cartesian Product of two fuzzynormed spaces is presented. Some basic properties and theorems on thisconcept are proved. The main goal of this paper is to prove that theCartesian product of two complete fuzzy normed spaces is a completefuzzy normed space.Key words:Fuzzy normed space , Cartesian product , Cauchy sequence ,complete fuzzy normed space.1- Introduction The fuzzy set concepts was introduced in mathematics by K.Mengerin 1942 and reintroduced in the system theory by L.A.Zadeh in 1965.In 1984, Katsaras [ 1 ] , first introduced the notation of fuzzy norm onlinear space, in the same year Wu and Fang [ 4 ] also introduced a notion offuzzy normed space . Later on many other mathematicians like Felbin [ 2 ], Cheng and Mordeson [ 10] , Bag and Samanta [12], J.Xiao and X.Zhu[8,9] , Krishna and Sarma [11] , Balopoulos and Papadopoulos [ 13] etc,have given different definitions of fuzzy normed spaces .J.Kider introduced the definition of fuzzy normed space[ 7 ] , we use thisdefinition to prove that the Cartesian product of two fuzzy normed spacesis also fuzzy normed space. The structure of the paper is as follow : In section 2 wepresent some fundamental concepts . In section 3, the definition of fuzzynormed space appeared [7] is used to prove that the cartesain product oftwo fuzzy normed spaces is also fuzzy normed space, then we prove thatthe cartesain product of two complete fuzzy normed spaces is completefuzzy normed space. 2. PreliminariesIn this section, we briefly recall some definitions and preliminaryresults which are used in this paper.