arXiv subjects

Sugata Adhya

Publications and source records attributed to Sugata Adhya.

6 recordsLinked to original sources

arXiv2023

Lebesgue Property and $G$-completeness in Generalized Quasi-uniform Spaces

This paper extends the Lebesgue property and (weak) $G$-completeness to generalized quasi-uniform spaces. It investigates the connections between completeness, (weak) $G$-completeness, and the Lebesgue property of the product of generalized quasi-uniform spaces with those of the component spaces. It has been observed that the related behaviors differ for the Lebesgue property in contrast to completeness and (weak) $G$-completeness.

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arXiv2023

On a Generalization of Quasi-metric Space

We find an extension of the quasi-metric (to be called $g$-quasi metric) such that the induced generalized topology may fail to form a topology. We show that $g$-quasi metrizability is a $g$-topologically invariant property of generalized topological spaces. Extending metric product and uniform continuity for $g$-quasi metric spaces, we note that a $g$-quasi metric may fail to be uniformly continuous in the extended sense unlike usual metric. Finally, we extend the study of completeness, Lebesgue property and weak $G$-completeness for $g$-quasi metric spaces.

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arXiv2021

Common Fixed Point Theorems on Complete and Weak $G$-Complete Fuzzy Metric Spaces

Motivated by Gopal and Vetro [Iranian Journal of Fuzzy Systems, 11(3), 95-107], we introduce a symmetric pair of $\beta$-admissible mappings and obtain common fixed point theorems for such a pair in complete and weak $G$-complete fuzzy metric spaces. In particular, we rectified, generalize and improve the common fixed point theorem obtained by Turkoglu and Sangurlu [Journal of Intelligent & Fuzzy Systems, 26(1), 137-142] for two fuzzy $\psi$-contractive mappings. We include non-trivial examples to exhibit the generality and demonstrate our results.

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arXiv2020

On Weak $G$-Completeness for Fuzzy Metric Spaces

In this paper, we provide equivalent characterizations of weak $G$-complete fuzzy metric spaces. Since such spaces are complete, we also characterize fuzzy metric spaces that have weak $G$-complete fuzzy metric completions. Moreover we establish analogous results for classical metric spaces.

math.GN↗

arXiv2020

Some Properties of Lebesgue Fuzzy Metric Spaces

In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak G-complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several well-known fuzzy metric spaces.

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arXiv2018

On Lebesgue Property for Fuzzy Metric Spaces

We provide several characterizations of the Lebesgue property for fuzzy metric spaces. It is known that a fuzzy metric space is Lebesgue if and only if every real-valued continuous function is uniformly continuous. Here we show that it suffices to examine uniform continuity of bounded real-valued continuous functions for characterizing Lebesgue property in fuzzy setting.

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