Korovkin type approximation theorems obtained through generalized statistical convergence
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TLDR
This work applies the generalized de la Vallee Poussin mean method to prove some Korovkin type approximation theorems and introduces the concept of λ -statistical convergence.About:
This article is published in Applied Mathematics Letters.The article was published on 2010-11-01 and is currently open access. It has received 93 citations till now. The article focuses on the topics: Modes of convergence & Normal convergence.read more
Citations
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Generalized weighted statistical convergence and application
TL;DR: A Korovkin type approximation theorem through statistical summability (N@?"@l,p) is determined and it is shown that the approximation theorem is stronger than classical Korvkin theorem by using classical Bernstein polynomials.
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A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean
TL;DR: A Korovkin type theorem is proved for the test functions 1, cosx,sinx in the space C"2"@p(R) of all continuous [email protected] functions on the real line R to prove the de la Vallee Poussin mean.
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Generalized equi-statistical convergence of positive linear operators and associated approximation theorems
TL;DR: The new notion of λ -equi-statistical convergence is applied to prove a Korovkin type approximation theorem and it is shown that the theorem is a non-trivial extension of some well-known Korovkins type approximation theorems.
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An application of almost convergence in approximation theorems
TL;DR: This work applies the Lorentz method to prove some Korovkin type approximation theorems of almost convergence, which have various applications in theory and practice.
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Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems
TL;DR: In this paper, the authors introduced the notions of weighted lacunary statistical pointwise and uniform convergence and a kind of convergence which is lying between aforementioned convergence methods, and obtained various implication results with supporting examples.
References
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Some approximation theorems via statistical convergence
A. D. Gadjiev,Cihan Orhan +1 more
TL;DR: In this paper, the authors prove some Korovkin and Weierstrass type approximation theorems via statistical convergence, and they also consider the order of statistical convergence of a sequence of positive linear operators.