DOI: 10.15672/hujms.1938717 ISSN: 2651-477X

Ideal $\alpha \beta $-statistical equal convergence and its application to Korovkin theorem

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In this paper, we introduce the notion of ideal $\alpha \beta $-statistical type convergence for sequences of real-valued functions, which unifies and extends both ideal $\alpha \beta $-statistical convergence and equal convergence. We also define the concept of ideal $\alpha \beta $-statisticalequal $\mathcal{A}$-summability by combining a regular summability method with an admissible ideal and fundamental algebraic properties are investigated. The relationships among these newly introduced notions are discussed and illustrated by an example. As an application, we establish a Korovkin-type approximation theorem within the framework of monotone sublinear operators. The theorem not only includes classical positive linear operators but also provides stronger convergence results under moregeneral assumptions. Finally, we construct Choquet-type of Szász-Mirakjan-Kantorovich-Chlodovsky that satisfy our Korovkin-type result but do not fulfill the classical Korovkin conditions, confirming the novelty of the proposed framework.

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