TY - JOUR
T1 - Strong approximation by Marcinkiewicz means of two-dimensional Walsh–Kaczmarz–Fourier series
AU - Goginava, U.
AU - Nagy, K.
N1 - Publisher Copyright:
© 2016, Akadémiai Kiadó, Budapest, Hungary.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.
AB - In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.
KW - Marcinkiewicz mean
KW - strong approximation
KW - Walsh–Kaczmarz function
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U2 - 10.1007/s10476-016-0203-0
DO - 10.1007/s10476-016-0203-0
M3 - Article
AN - SCOPUS:84978259263
SN - 0133-3852
VL - 42
SP - 143
EP - 157
JO - Analysis Mathematica
JF - Analysis Mathematica
IS - 2
ER -