Babenko, V. F.; Parfinovych, N. V.; Pichugov, S. A. Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions. (English) Zbl 1224.41041 Ukr. Mat. Zh. 62, No. 3, 301-314 (2010) and in Ukr. Math. J. 62, No. 3, 343-357 (2010). MSC: 41A17 26D10 26A33 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 62, No. 3, 301--314 (2010; Zbl 1224.41041) Full Text: DOI Link
Babenko, V. F.; Pichugov, S. A. On Kolmogorov-type inequalities for fractional derivatives of functions of two variables. (Russian, English) Zbl 1164.26322 Ukr. Mat. Zh. 60, No. 6, 837-842 (2008); translation in Ukr. Math. J. 60, No. 6, 977-984 (2008). MSC: 26B05 26D10 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{S. A. Pichugov}, Ukr. Mat. Zh. 60, No. 6, 837--842 (2008; Zbl 1164.26322); translation in Ukr. Math. J. 60, No. 6, 977--984 (2008) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Exact inequalities for derivatives of functions of low smoothness defined on an axis and a semiaxis. (Russian, English) Zbl 1105.41009 Ukr. Mat. Zh. 58, No. 3, 291-302 (2006); translation in Ukr. Math. J. 58, No. 3, 325-339 (2006). MSC: 41A17 26D15 41A44 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 58, No. 3, 291--302 (2006; Zbl 1105.41009); translation in Ukr. Math. J. 58, No. 3, 325--339 (2006) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Approximation of sine-shaped functions by constants in spaces \(L_p,p<1\). (Russian, English) Zbl 1089.41010 Ukr. Mat. Zh. 56, No. 6, 745-762 (2004); translation in Ukr. Math. J. 56, No. 6, 882-903 (2004). MSC: 41A30 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 56, No. 6, 745--762 (2004; Zbl 1089.41010); translation in Ukr. Math. J. 56, No. 6, 882--903 (2004) Full Text: DOI
Babenko, V. F.; Kornejchuk, N. P.; Pichugov, S. A. Kolmogorov-type inequalities for mixed derivatives of multivariate functions. (Russian, English) Zbl 1089.41003 Ukr. Mat. Zh. 56, No. 5, 579-594 (2004); translation in Ukr. Math. J. 56, No. 5, 699-717 (2004). MSC: 41A17 26D15 41A44 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 56, No. 5, 579--594 (2004; Zbl 1089.41003); translation in Ukr. Math. J. 56, No. 5, 699--717 (2004) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Comparison of exact constants in inequalities for derivatives of functions defined on the real axis and a circle. (Russian, English) Zbl 1103.26013 Ukr. Mat. Zh. 55, No. 5, 579-589 (2003); translation in Ukr. Math. J. 55, No. 5, 699-711 (2003). Reviewer: A. M. Gomilko (Kyïv) MSC: 26D10 41A17 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 55, No. 5, 579--589 (2003; Zbl 1103.26013); translation in Ukr. Math. J. 55, No. 5, 699--711 (2003) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. On Kolmogorov-type inequalities with integrable higher derivatives. (Ukrainian. English summary) Zbl 1025.26011 Ukr. Mat. Zh. 54, No. 12, 1694-1697 (2002). MSC: 26D10 41A17 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 54, No. 12, 1694--1697 (2002; Zbl 1025.26011) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Kolmogorov-type inequalities for periodic functions whose first derivatives have bounded variation. (English. Russian original) Zbl 1015.41009 Ukr. Math. J. 54, No. 5, 741-749 (2002); translation from Ukr. Mat. Zh. 54, No. 5, 603-609 (2002). Reviewer: A.M.Gomilko (Kyïv) MSC: 41A17 26D10 26A45 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 54, No. 5, 603--609 (2002; Zbl 1015.41009); translation from Ukr. Mat. Zh. 54, No. 5, 603--609 (2002) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Exact Kolmogorov-type inequalities with bounded leading derivative in the case of low smoothness. (English. Russian original) Zbl 1008.41011 Ukr. Math. J. 53, No. 10, 1569-1582 (2001); translation from Ukr. Mat. Zh. 53, No. 10, 1299-1308 (2001). Reviewer: A.M.Gomilko (Kyïv) MSC: 41A17 26D10 41A15 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 53, No. 10, 1299--1308 (2001; Zbl 1008.41011); translation from Ukr. Mat. Zh. 53, No. 10, 1299--1308 (2001) Full Text: DOI
Pichugov, S. A. On the Jackson theorem for periodic functions in spaces with integral metric. (English. Russian original) Zbl 0987.42002 Ukr. Math. J. 52, No. 1, 133-147 (2000); translation from Ukr. Mat. Zh. 52, No. 1, 122-133 (2000). MSC: 42A10 42B99 41A17 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 52, No. 1, 122--133 (2000; Zbl 0987.42002); translation from Ukr. Mat. Zh. 52, No. 1, 122--133 (2000) Full Text: DOI
Kornejchuk, N. P.; Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Inequalities for upper bounds of functionals on the classes \(W^rH^{\omega}\) and some of their applications. (English. Russian original) Zbl 0987.42003 Ukr. Math. J. 52, No. 1, 71-90 (2000); translation from Ukr. Mat. Zh. 52, No. 1, 66-84 (2000). MSC: 42A10 41A17 42A05 PDFBibTeX XMLCite \textit{N. P. Kornejchuk} et al., Ukr. Mat. Zh. 52, No. 1, 66--84 (2000; Zbl 0987.42003); translation from Ukr. Mat. Zh. 52, No. 1, 66--84 (2000) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Comparison of approximation properties of generalized polynomials and splines. (English. Russian original) Zbl 0946.41016 Ukr. Math. J. 50, No. 8, 1151-1161 (1998); translation from Ukr. Mat. Zh. 50, No. 8, 1011-1020 (1998). MSC: 41A50 41A15 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 50, No. 8, 1011--1020 (1998; Zbl 0946.41016); translation from Ukr. Mat. Zh. 50, No. 8, 1011--1020 (1998) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. On additive inequalities for intermediate derivatives of functions given on a finite interval. (English. Russian original) Zbl 0935.26004 Ukr. Math. J. 49, No. 5, 685-696 (1997); translation from Ukr. Mat. Zh. 49, No. 5, 619-628 (1997). Reviewer: Yu.V.Kozachenko (Kyïv) MSC: 26D10 41A17 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 49, No. 5, 619--628 (1997; Zbl 0935.26004); translation from Ukr. Mat. Zh. 49, No. 5, 619--628 (1997) Full Text: DOI
Pichugov, S. A. Approximation in measure of measurable periodic functions by piece-wise constant functions. (Russian) Zbl 0887.41016 Ukr. Mat. Zh. 48, No. 5, 711-715 (1996). Reviewer: A.A.Martynyuk (Kyïv) MSC: 41A20 41A27 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 48, No. 5, 711--715 (1996; Zbl 0887.41016) Full Text: DOI
Pichugov, S. A. Approximation of measurable periodic functions in measure by step functions. (English. Russian original) Zbl 0932.41012 Ukr. Math. J. 48, No. 5, 795-800 (1996); translation from Ukr. Mat. Zh. 48, No. 5, 711-715 (1996). MSC: 41A20 41A27 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 48, No. 5, 711--715 (1996; Zbl 0932.41012); translation from Ukr. Mat. Zh. 48, No. 5, 711--715 (1996) Full Text: DOI
Pichugov, S. A. Approximation of periodic function compressions in the space \(L_ p, p<1\). (Russian) Zbl 0887.42003 Ukr. Mat. Zh. 47, No. 12, 1708-1711 (1995). MSC: 42A10 41A65 41A50 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 47, No. 12, 1708--1711 (1995; Zbl 0887.42003) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. On inequalities for norms of intermediate derivatives on a finite interval. (English. Russian original) Zbl 0887.26009 Ukr. Math. J. 47, No. 1, 121-124 (1995); translation from Ukr. Mat. Zh. 47, No. 1, 105-107 (1995). Reviewer: A.D.Borisenko (Kyïv) MSC: 26D10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 47, No. 1, 105--107 (1995; Zbl 0887.26009); translation from Ukr. Mat. Zh. 47, No. 1, 105--107 (1995) Full Text: DOI
Pichugov, S. A. Approximation of periodic functions by constants in the metric spaces \(\varphi (L)\). (English. Russian original) Zbl 0851.41030 Ukr. Math. J. 46, No. 8, 1206-1209 (1994); translation from Ukr. Mat. Zh. 46, No. 8, 1095-1098 (1994). MSC: 41A65 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 46, No. 8, 1095--1098 (1994; Zbl 0851.41030); translation from Ukr. Mat. Zh. 46, No. 8, 1095--1098 (1994) Full Text: DOI
Pichugov, S. A. Approximation of periodic functions by a constant in metric spaces \(\varphi (L)\). (Russian. English summary) Zbl 0841.41032 Ukr. Mat. Zh. 46, No. 8, 1095-1098 (1994). Reviewer: I.Serb (Cluj-Napoca) MSC: 41A65 PDFBibTeX XMLCite \textit{S. A. Pichugov}, Ukr. Mat. Zh. 46, No. 8, 1095--1098 (1994; Zbl 0841.41032) Full Text: DOI
Ganzburg, M. I.; Pichugov, S. A. On the invariance of elements of best approximation and a certain theorem of Glaeser. (Russian) Zbl 0482.41020 Ukr. Mat. Zh. 33, 664-667 (1981). MSC: 41A50 PDFBibTeX XMLCite \textit{M. I. Ganzburg} and \textit{S. A. Pichugov}, Ukr. Mat. Zh. 33, 664--667 (1981; Zbl 0482.41020)