TY - JOUR
T1 - Fuzzy n−Controlled Metric Space
AU - Furqan, Salman
AU - Saleem, Naeem
AU - Sessa, Salvatore
N1 - Publisher Copyright:
© 2023 the author(s).
PY - 2023
Y1 - 2023
N2 - This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is given to prove the uniqueness of the solution to fractional differential equations.
AB - This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is given to prove the uniqueness of the solution to fractional differential equations.
KW - controlled metric space
KW - fixed point
KW - fractional differential equation
KW - fuzzy metric space
UR - http://www.scopus.com/inward/record.url?scp=85172295017&partnerID=8YFLogxK
U2 - 10.28924/2291-8639-21-2023-101
DO - 10.28924/2291-8639-21-2023-101
M3 - Article
AN - SCOPUS:85172295017
SN - 2291-8639
VL - 21
JO - International Journal of Analysis and Applications
JF - International Journal of Analysis and Applications
M1 - 101
ER -