Yazarlar

• Atıcı Turan, Gülcan(1)
• Et, Mikail(1)
• Turan, Gulcan Atici(1)

• MakaleAçık Erişim2025/r/munzur/4397
  On Wijsman fρ-Statistical Convergence of Order α of Modulus Functions

  Turan, Gulcan Atici; Et, Mikail

  In the present paper, we introduce and investigate the concepts of Wijsman f rho-statistical convergence of order alpha and Wijsman strong f rho-convergence of order alpha. 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 f rho-statistical convergence and Wijsman strong f rho-convergence of order alpha, 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 alpha, and the sequence rho. 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.

  AtıfWoS1·OpenAlex1

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• MakaleAçık Erişim2025Scopus SJRQ2/r/munzur/1418
  Generalized Statistical Convergence in Sequence Spaces: A Modulus Function Perspective

  Atıcı Turan, Gülcan

  This study introduces a flexible framework for analyzing how sequences of numbers approach a limit, even when traditional convergence criteria fail. By incorporating modulus function mathematical tools that quantify growth rates, this research extends the concept of statistical convergence to handle sequences with irregular or sparse behavior. Key results establish connections between this generalized convergence theory and related properties, like boundedness, providing a unified approach to understanding sequence dynamics. The findings enhance our ability to model and analyze complex data patterns in mathematics and beyond.

  AtıfScopus1·WoS2·OpenAlex3

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