Modulative categories and fixed point theorems on modulative metric spaces

Abstract

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.

Keywords

• Enriched category
• fixed point
• Lawvere quantale
• modulative metric space

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