Open AccessKorovkin type approximation theorem for functions of two variables in statistical sense
Author(s) -
Fadime Dirik,
Kami̇l Demi̇rci̇
Publication year - 2010
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-0802-21
Subject(s) - mathematics , type (biology) , operator (biology) , unbounded operator , linear operators , convergence (economics) , space (punctuation) , discrete mathematics , pure mathematics , mathematical analysis , approximation property , banach space , ecology , biochemistry , chemistry , linguistics , philosophy , repressor , biology , transcription factor , economics , bounded function , gene , economic growth
In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables