TY - JOUR
T1 - Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type
AU - Vakarchuk, Sergey B.
JF - International Journal of Advanced Research in Mathematics
VL - 6
SP - 1
EP - 12
SN - 2297-6213
PY - 2016
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/IJARM.6.1
UR - https://www.scipress.com/IJARM.6.1
KW - Best Approximations
KW - Entire Function of Exponential Type
KW - K-Functional
KW - Majorant
KW - Mean v-Width
AB - K-functionals K (f, t, L2(R), L2β(R), which defined by the fractional derivatives of order β>0, have been considered in the space L2(R). The relation K (f, tβ, L2(R), L2β(R) ≈ ωβ (f, t) (t>0) was obtained in the sense of the weak equivalence, where ωωβ (f, t) is the module of continuity of the fractional order β for a function f є L2(R). Exact values of the best approximation by entire functions of exponential type v∏, v є (0, ∞) have been computed for the classes of functions, given by the indicated K-functionals and majorants Ψ satisfying specific restriction. Kolmogorov, Bernsteinand linear mean v-widths were obtained for indicated classes of functions.
ER -