Approximation of classes of periodic multivariable functions by linear positive operators |
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Authors: | D M Bushev Yu I Kharkevych |
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Institution: | (1) Volyn University, Lutsk |
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Abstract: | In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator
whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation
does not exceed the sum of properly chosen least upper bounds in m-and ((N − m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 12–19, January, 2006. |
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