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.
📌 3 Key Takeaways
🎯
Objective & Hypothesis: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.
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Key Findings & Data:We obtain some results on modulative metric spaces and modulative categories, and illustrate them with examples.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Enriched category · fixed point · Lawvere quantale
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.
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