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.
abstract Korovkin theorem double sequence filter convergence matrix summability modular spaces
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 6 Ağustos 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 50 Sayı: 4 |