Theorems for generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces |
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| Authors: | Grzegorz Nowak Aneta Sikorska-Nowak |
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| Institution: | (1) Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University, 560 Toyonaka, Osaka, Japan;(2) Present address: Cognitive Processes Department, ATR Auditory and Visual Perception Research Laboratories, Twin 21 Bldg. MID Tower, 540 Osaka, Japan;(3) Present address: Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo, 113 Tokyo, Japan; |
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| Abstract: | We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove some direct
approximation theorems for functions f such that w
σ
f ∈ L
p
(R), where 1 ≤ p ≤ ∞ and w
σ
(x) = exp(−σx
2), σ > 0. |
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| Keywords: | |
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