Geodesic
Equi-statistical convergence of a sequence of distribution functions via deferred Nörlund summability mean and associated approximation theorems
Filomat, Tome 35 (2021) no. 13, p. 4501

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In this paper, the notion of statistical point-wise convergence, equi-statistical convergence and statistical uniform convergence of a sequence of distribution functions via the deferred Nörlund summability mean has been introduced, and accordingly an inclusion relation between these interesting notions is established. Moreover, as an application point of view, a new Korovkin-type approximation theorem is proved via the deferred Nörlund equi-statistical convergence for the sequence of distribution functions. Also, some illustrative examples are considered to justify that the proposed theorem is a nontrivial extension of some well established Korovkin-type approximation theorems for sequence of real-valued functions. Finally, a number of interesting cases are highlighted in support of the definitions and outcomes
DOI : 10.2298/FIL2113501J
Classification : 40A05, 40G15, 41A36
Keywords: Sequence of random variables, Equi-statistical convergence, Deferred Nörlund mean, Distribution functions, Positive linear operator, Korovkin-type approximation theorem 
Bidu Bhusan Jena. Equi-statistical convergence of a sequence of distribution functions via deferred Nörlund summability mean and associated approximation theorems. Filomat, Tome 35 (2021) no. 13, p. 4501 . doi: 10.2298/FIL2113501J
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     title = {Equi-statistical convergence of a sequence of distribution functions via deferred {N\"orlund} summability mean and associated approximation theorems},
     journal = {Filomat},
     pages = {4501 },
     year = {2021},
     volume = {35},
     number = {13},
     doi = {10.2298/FIL2113501J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2113501J/}
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