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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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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