Geodesic
A-statistical convergence with a rate and applications to approximation
Filomat, Tome 36 (2022) no. 15, p. 5323

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DOI

A = (a nk) be a regular summability matrix. In the present paper we deal with subspaces of the space of A−statistically convergent sequences obtained by the rate at which the A−statistical limit tends to zero. We prove that a sequence is the A−strongly convergent if and only if it is the A−statistically convergent and the A−uniformly integrable with the rate of o (a n) where a = (a n) is a positive nonincreasing sequence. We also make a link between the A−strong convergence and the A−distributional convergence with the rate of o (a n). Finally, as an application we present an approximation theorem of Korovkin type.
DOI : 10.2298/FIL2215323G
Classification : 40A35, 40G15, 40F05, 60B10, 41A36
Keywords: Density, Statistical convergence, Uniform integrability, Strong convergence, Distributional convergence, Korovkin type approximation 
Mustafa Gülfırat. A-statistical convergence with a rate and applications to approximation. Filomat, Tome 36 (2022) no. 15, p. 5323 . doi: 10.2298/FIL2215323G
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     author = {Mustafa G\"ulf{\i}rat},
     title = {A-statistical convergence with a rate and applications to approximation},
     journal = {Filomat},
     pages = {5323 },
     year = {2022},
     volume = {36},
     number = {15},
     doi = {10.2298/FIL2215323G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2215323G/}
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