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Keywords = Wijsman statistical convergence

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15 pages, 313 KB  
Article
On Wijsman fρ-Statistical Convergence of Order α of Modulus Functions
by Gülcan Atıcı Turan and Mikail Et
Axioms 2025, 14(10), 730; https://doi.org/10.3390/axioms14100730 - 26 Sep 2025
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Abstract
In the present paper, we introduce and investigate the concepts of Wijsman fρ-statistical convergence of order α and Wijsman strong fρ-convergence of order α. These notions are defined as natural generalizations of classical statistical convergence and Wijsman convergence, [...] Read more.
In the present paper, we introduce and investigate the concepts of Wijsman fρ-statistical convergence of order α and Wijsman strong fρ-convergence of order α. These notions are defined as natural generalizations of classical statistical convergence and Wijsman convergence, incorporating the tools of modulus functions and natural density through the function f. We provide a detailed analysis of their structural properties, including inclusion relations, basic characterizations, and illustrative examples. Furthermore, we establish the inclusion relations between Wijsman fρ-statistical convergence and Wijsman strong fρ-convergence of order α, showing conditions under which one implies the other. These notions are different in general, while coinciding under certain restrictions on the function f, the parameter α, and the sequence ρ. The results obtained not only extend some well-known findings in the literature but also open up new directions for further study in the theory of statistical convergence and its applications to analysis and approximation theory. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
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