What question did this study set out to answer?

To explore the concept of statistical forward quasi Cauchy sequences in asymmetric metric spaces and their relation to total boundedness.

February 14, 2026Open Access

Statistical quasi Cauchyness on asymmetric spaces

Key Points

To explore the concept of statistical forward quasi Cauchy sequences in asymmetric metric spaces and their relation to total boundedness.
Defined statistical forward quasi Cauchy sequences in asymmetric spaces.
Proved a equivalence of total boundedness and quasi Cauchy subsequences.
Investigated statistical upward continuity for functions mapping between spaces.
A subset of an asymmetric space is totally bounded if all sequences within it have a statistically forward quasi Cauchy subsequence.
Introduced the concept of statistical upward continuity, showing its relevance to quasi Cauchy sequences.

Abstract

We call a sequence (xₘ) of points in an asymmetric metric space (X, d) statistically forward quasi Cauchy if ₍ 1n | \m n: d (xₘ, x₌+₁) \ | = 0 for each positive, where |A| indicates the cardinality of the set A. We prove that a subset E of X is forward totally bounded if and only if any sequence of points in E has a statistically forward quasi Cauchy subsequence. We also introduce and investigate statistically upward continuity in the sense that a function defined on X into Y is called statistically upward continuous if it preserves statistically forward quasi Cauchy sequences, i. e. (f (xₘ) ) is statistically forward quasi Cauchy whenever (xₘ) is.

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Cite This Study

Fikriye Ince Dagci (Wed,) studied this question.

synapsesocial.com/papers/6990113f2ccff479cfe57b70 https://doi.org/https://doi.org/10.2298/fil2518383d

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