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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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

İncele

Atıcı Turan, Gülcan; Polat, Fatma

In this study, we examined some fixed point theorems in non-full metric spaces. We define the notions of α-lower semi-continuous , w-α-distance, w_0-α– distance, w-α-rational contraction and generalized w-α-rational contraction mapping. We also give related theorem and example. Then, we prove Banach’s fixed-point theorem thanks to the concept w-α- distance in metric spaces equipped with an abritrary binary relation. Also, w-α- rational contraction mapping and generalized w-α-rational contraction mapping are defined and by using these definitions, the theorem related fixed point is expressed and proved.

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