Some approximation theorems via statistical convergence

By A. D. Gadjiev, Cihan Orhan. 2002

554 citations recorded by the source corpus.

In this paper we prove some Korovkin and Weierstrass type approximation theorems via statistical convergence. We are also concerned with the order of statistical convergence of a sequence of positive linear operators.

Subfields: Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8b97b423dcd56679d4a4a33cb082dd66c4c4a17a

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In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Equi-statistical convergence of positive linear operators (2008, methodology): “However, since (gn) is not statistically uniform convergent to the function g = 0 on the interval [0,1], we can say that Theorem 1 of [11] does not work for our operators defined by (2.”
Lacunary statistical convergence and strongly lacunary summable functions of order α (2017, unknown): “Later on it was further investigated from the sequence space viewpoint and linked with summability theory by Alotaibi and Alroqi [1], Çolak [5], Connor [6], Et et al. ([9], [10] and [11]), Fridy [14], Gadjiev and Orhan [16], Güngör et al. ([17] and [18]), Mohiuddine et al. [19], Mursaleen and Alo”
Korovkin-type Theorems and Approximation by Positive Linear Operators (2010, unknown): “, in [1], [9-15], [22], [47-52], [63], [71-74], [79], [114-116], [117] and the references therein.”
Statistical approximation by positive linear operators (2004, background): “Recently, its use in approximation theory has been considered in [6], [13].”
Abstract Korovkin-type theorems in modular spaces and applications (2013, methodology): “Our results extend Korovkin-type theorems given in [8, 10, 17, 18] in the context of modular spaces and in [16] in the setting of ideal convergence.”
Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems (2019, unknown): “The Korovkin result, in statistical sense, firstly was proved in [21].”
Generalized -Bernstein-Schurer Operators and Some Approximation Theorems (2013, unknown): “[18] A. D. Gadjiev and C. Orhan, “Some approximation theorems via statistical convergence,” Rocky Mountain Journal of Mathematics, vol. 32, no. 1, pp. 129–138, 2002.”
Statistical approximation properties of Kantorovich operators based on q-integers (2008, background): “We denote this limit by st− lim n xn = L (see [9], [8], [16]).”