Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this paper, we first introduce the notions of $\mathcal{F-}$relative modular convergence and $\mathcal{F-}$relative strong convergence for double sequences of functions.
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Temel Bulgular & Veri:Also, we present a non-trivial application such that our Korovkin-type approximation results in modular spaces are stronger than the classical ones and we present some estimates of rates of convergence for abstract Korovkin-type theorems.
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Sonuç & Katkı:Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.
In this paper, we first introduce the notions of $\mathcal{F-}$relative modular convergence and $\mathcal{F-}$relative strong convergence for double sequences of functions. Then we prove some Korovkin-type approximation theorems via $\mathcal{F-}$relative $\mathcal{A}-$summation process on modular spaces for double sequences of positive linear operators. Also, we present a non-trivial application such that our Korovkin-type approximation results in modular spaces are stronger than the classical ones and we present some estimates of rates of convergence for abstract Korovkin-type theorems. Furthermore, we relax the positivity condition of linear operators in the Korovkin theorems and study an extension to non-positive operators.
Yıldız, S. (2022). $\mathcal{F-}$relative $\mathcal{A-}$summation process for double sequences and abstract Korovkin type theorems. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1047–1062. https://ajindex.com/articles/529973
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