TY  - JOUR
T1  - Modulative Categories and Fixed Point Theorems on Modulative Metric Spaces
AU  - Uyanık Ekici, Elif
AU  - Gürdal, Utku
AU  - Çetin, Selim
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.15672/hujms.1643663
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1
EP  - 21
LA  - en
AB  - In terms of enriched category theory, we obtain a categorical explanation of the concept of modular metric spaces, similar to the case of Lawvere metric spaces. To this end, we introduce a generalization of categories that we call modulative categories, and as an extension of this, we define a new concept of modulative metric spaces along with several other notions. We obtain some results on modulative metric spaces and modulative categories, and illustrate them with examples. Finally, we develop a theory of convergence in modulative metric spaces and generalize some fixed-point theorems to demonstrate the applicability of the results obtained.
KW  - Enriched category
KW  - Fixed point
KW  - Lawvere quantale
KW  - Modulative metric space
CR  - [1] J. Adámek, H. Herrlich and G. Strecker, Abstract and concrete categories, Dover
Publications, Mineola, New York, 2009.
UR  - https://doi.org/10.15672/hujms.1643663
L1  - https://dergipark.org.tr/en/download/article-file/4626554
ER  -