Korovkin-Type Theorems for Modular<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>Ψ</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:math>-Statistical Convergence

Carlo Bardaro, Antonio Boccuto, Kami̇l Demi̇rci̇, Ilaria Mantellını, Sevda Orhan

Type: Article

Publication Date: 2015-01-01

Citations: 20

DOI: https://doi.org/10.1155/2015/160401

Abstract

We deal with a new type of statistical convergence for double sequences, called<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>Ψ</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:math>-statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces.

Locations

Journal of Function Spaces - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View
INFM-OAR (INFN Catania) - View - PDF

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Works Cited by This (42)

Action	Title	Year	Authors
+	Generalized sampling operators in modular spaces	1998	Ilaria Mantellini
+	Korovkin-type Approximation Theory and its Applications	1994	Francesco Altomare Michele Campıtı
+	Korovkin type approximation theorem for functions of two variables in statistical sense	2010	Fadime Dirik Kami̇l Demi̇rci̇
+	Statistical approximation in multivariate modular function spaces	2011	Cemal Belen Mustafa Yıldırım
+	A-statistical convergence of subsequence of double sequences	2007	Harry I. Miller
+	On the asymptotic behaviour of linear combinations of Mellin‐Picard type operators	2013	Ilaria Mantellını
+	A general approximation result for nonlinear integral operators and applications to signal processing<sup>*</sup>	2001	Gianluca Vıntı
+	Statistical $$\fancyscript{A}$$ A -summation process and Korovkin type approximation theorem on modular spaces	2013	Sevda Orhan Kami̇l Demi̇rci̇
+	A direct approach to the mellin transform	1997	P. L. Butzer Stefan Jansche
+	Korovkin theorems in Lp-spaces	1981	Klaus Donner