Open AccessFixed Point Theory in Fuzzy Normed Linear Spaces: A General View
Author(s) -
Simona Dziţac,
Horea Oros,
Dan Deac,
Sorin Nădăban
Publication year - 2021
Publication title -
international journal of computers, communications and control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.422
H-Index - 33
eISSN - 1841-9844
pISSN - 1841-9836
DOI - 10.15837/ijccc.2021.6.4587
Subject(s) - mathematics , fuzzy logic , banach space , metric space , discrete mathematics , fixed point theorem , completeness (order theory) , context (archaeology) , t norm , fixed point , normed vector space , fuzzy set , fuzzy number , pure mathematics , algebra over a field , computer science , mathematical analysis , artificial intelligence , paleontology , biology
In this paper we have presented, firstly, an evolution of the concept of fuzzy normed linear spaces, different definitions, approaches as well as generalizations. A special section is dedicated to fuzzy Banach spaces. In the case of fuzzy normed linear spaces, researchers have been working, until now, with a definition of completeness inspired by M. Grabiec’s work in the context of fuzzy metric spaces. We propose another definition and we prove that it is much more adequate, inspired by the work of A.George and P. Veeramani. Finally, some important results in fuzzy fixed point theory were highlighted.