Babushkin, M. V.; Zhuk, V. V. On the strong form of asymptotic formulas of the Voronovskaya-Bernstein type with a pointwise estimate of the remainder term. (English. Russian original) Zbl 1377.41007 J. Math. Sci., New York 225, No. 6, 859-876 (2017); translation from Zap. Nauchn. Semin. POMI 449, 32-59 (2016). MSC: 41A25 26A15 41A35 41A36 PDFBibTeX XMLCite \textit{M. V. Babushkin} and \textit{V. V. Zhuk}, J. Math. Sci., New York 225, No. 6, 859--876 (2017; Zbl 1377.41007); translation from Zap. Nauchn. Semin. POMI 449, 32--59 (2016) Full Text: DOI
Vinogradov, O. L.; Zhuk, V. V. Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences. (English. Russian original) Zbl 1262.41010 J. Math. Sci., New York 184, No. 6, 679-698 (2012); translation from Zap. Nauchn. Semin. POMI 392, 32-66 (2011). Reviewer: Radu Păltănea (Braşov) MSC: 41A17 41A25 41A44 41A45 41A50 41A10 26A15 42A10 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, J. Math. Sci., New York 184, No. 6, 679--698 (2012; Zbl 1262.41010); translation from Zap. Nauchn. Semin. POMI 392, 32--66 (2011) Full Text: DOI
Vinogradov, O. L.; Zhuk, V. V. Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means. (English. Russian original) Zbl 1303.41006 J. Math. Sci., New York 178, No. 2, 115-131 (2011); translation from Zap. Nauchn. Semin. POMI 383, 5-32 (2010). MSC: 41A17 26D15 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, J. Math. Sci., New York 178, No. 2, 115--131 (2011; Zbl 1303.41006); translation from Zap. Nauchn. Semin. POMI 383, 5--32 (2010) Full Text: DOI
Vinogradov, O. L.; Zhuk, V. V. Estimates of errors of quadrature formulas by linear combinations of the uniform norm and oscillation of derivatives with both sharp constants. (English. Russian original) Zbl 1050.26022 J. Math. Sci., New York 117, No. 3, 4065-4095 (2003); translation from Probl. Mat. Anal. 26, 3-46 (2003). Reviewer: Yu. S. Volkov (Novosibirsk) MSC: 26D15 41A55 65D32 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, Probl. Mat. Anal. 26, 3--46 (2003; Zbl 1050.26022); translation from Probl. Mat. Anal. 26, 3--46 (2003)
Vinogradov, O. L.; Zhuk, V. V. Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines. (English. Russian original) Zbl 1078.42001 J. Math. Sci., New York 124, No. 2, 4845-4857 (2004); translation from Zap. Nauchn. Semin. POMI 290, 5-26 (2002). MSC: 42A10 41A17 41A15 26A15 26D10 41A50 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, J. Math. Sci., New York 124, No. 2, 4845--4857 (2002; Zbl 1078.42001); translation from Zap. Nauchn. Semin. POMI 290, 5--26 (2002) Full Text: DOI
Vinogradov, O. L.; Zhuk, V. V. Sharp estimates for the norms of differences in terms of the norms of the derivatives and the best majorants of moduli of continuity of periodic functions. (English. Russian original) Zbl 1050.41011 J. Math. Sci., New York 112, No. 1, 3967-3991 (2002); translation from Probl. Mat. Anal. 24, 61-94 (2002). Reviewer: V. Grebenev (Novosibirsk) MSC: 41A17 26A15 26A24 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, Probl. Mat. Anal. 24, 61--94 (2002; Zbl 1050.41011); translation from Probl. Mat. Anal. 24, 61--94 (2002)
Vinogradov, O. L.; Zhuk, V. V. Exact inequalities connected with estimates for approximations of periodic functions by continuity moduli of the derivatives of odd orders with various steps. (Russian, English) Zbl 1060.41502 Probl. Mat. Anal. 19, 69-88 (1999); translation in J. Math. Sci., New York 101, No. 2, 2914-2929 (2000). Reviewer: V. Grebenev (Novosibirsk) MSC: 41A17 41A30 42A16 26A15 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, Probl. Mat. Anal. 19, 69--88 (2000; Zbl 1060.41502); translation in J. Math. Sci., New York 101, No. 2, 2914--2929 (2000)
Vinogradov, O. L.; Zhuk, V. V. On the precision of a representation of the Steklov means of functions of two variables by means of singular integrals. (English. Russian original) Zbl 1043.42004 Vestn. St. Petersbg. Univ., Math. 32, No. 4, 9-17 (1999); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 1999, No. 4, 13-21 (1999). MSC: 42B05 26B30 42B08 PDFBibTeX XMLCite \textit{O. L. Vinogradov} and \textit{V. V. Zhuk}, Vestn. St. Petersbg. Univ., Math. 32, No. 4, 9--17 (1999; Zbl 1043.42004); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 1999, No. 4, 13--21 (1999)
Zhuk, V. V.; Natanson, G. I. Approximation of functions on standard simplexes. (English. Russian original) Zbl 0928.41003 Transl., Ser. 2, Am. Math. Soc. 188, 131-151 (1999); translation from Tr. St-Peterbg. Mat. Obshch. 4, 193-221 (1996). Reviewer: D.K.Ugulawa (Tbilisi) MSC: 41A10 41A25 26D10 41A30 PDFBibTeX XMLCite \textit{V. V. Zhuk} and \textit{G. I. Natanson}, Transl., Ser. 2, Am. Math. Soc. 188, 131--151 (1996; Zbl 0928.41003); translation from Tr. St-Peterbg. Mat. Obshch. 4, 193--221 (1996)
Zhuk, V. V. Seminorms and higher-order moduli of continuity. (English) Zbl 0848.42005 Transl., Ser. 2, Am. Math. Soc. 159, 77-122 (1994); translation from Tr. St-Peterbg. Mat. Obshch 2, 116-177 (1993). Reviewer: Y.A.Brudnyi (Haifa) MSC: 42A10 26A15 41A10 41A50 PDFBibTeX XMLCite \textit{V. V. Zhuk}, Transl., Ser. 2, Am. Math. Soc. 159, 77--122 (1993; Zbl 0848.42005); translation from Tr. St-Peterbg. Mat. Obshch 2, 116--177 (1993)
Zhuk, V. V.; Natanson, G. I. On approximation of functions on standard simplexes. (English. Russian original) Zbl 0786.41014 Russ. Acad. Sci., Dokl., Math. 45, No. 3, 614-618 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 324, No. 4, 734-737 (1992). MSC: 41A10 26A15 PDFBibTeX XMLCite \textit{V. V. Zhuk} and \textit{G. I. Natanson}, Russ. Acad. Sci., Dokl., Math. 45, No. 3, 1 (1992; Zbl 0786.41014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 324, No. 4, 734--737 (1992)
Zhuk, V. V. Some estimates for seminorms by means of moduli of continuity. (English) Zbl 0507.46021 Vestn. Leningr. Univ., Math. 14, 107-117 (1982). MSC: 46E10 26A15 46E15 42A10 42A16 PDFBibTeX XMLCite \textit{V. V. Zhuk}, Vestn. Leningr. Univ., Math. 14, 107--117 (1982; Zbl 0507.46021)
Zhuk, V. V. Some estimations for seminorms by means of moduli of continuity. (Russian) Zbl 0475.46020 Vestn. Leningr. Univ. 1981, No. 7, Mat. Mekh. Astron. 1981, No. 2, 29-37 (1981). MSC: 46E10 42A10 42A16 26A15 PDFBibTeX XMLCite \textit{V. V. Zhuk}, Vestn. Leningr. Univ., Mat. Mekh. Astron. 1981, No. 2, 29--37 (1981; Zbl 0475.46020)
Zhuk, V. V.; Natanson, G. I. On the question of approximation in an integral metric of functions defined on an interval. (English) Zbl 0471.41006 Vestn. Leningr. Univ., Math. 12, 169-182 (1980). MSC: 41A10 41A30 41A17 26A15 PDFBibTeX XMLCite \textit{V. V. Zhuk} and \textit{G. I. Natanson}, Vestn. Leningr. Univ., Math. 12, 169--182 (1980; Zbl 0471.41006)
Zhuk, V. V. On some sharp inequalities between functionals defined on sets of periodic functions and moduli of continuity. (English) Zbl 0437.42004 Vestn. Leningr. Univ., Math. 8, 199-205 (1980). MSC: 42A16 26A15 PDFBibTeX XMLCite \textit{V. V. Zhuk}, Vestn. Leningr. Univ., Math. 8, 199--205 (1980; Zbl 0437.42004)
Zhuk, V. V. Über einige genaue Ungleichungen zwischen Funktionalen, die auf Mengen periodischer Funktionen vorgegeben sind, und Stetigkeitsmoduln. (Russian) Zbl 0358.42003 Vestn. Leningr. Univ. 1975, No. 7, Mat. Mekh. Astron. 1975, No. 2, 29-34 (1975). MSC: 42A16 26A15 PDFBibTeX XMLCite \textit{V. V. Zhuk}, Vestn. Leningr. Univ., Mat. Mekh. Astron. 1975, No. 2, 29--34 (1975; Zbl 0358.42003)
Zhuk, V. V.; Natanson, G. I. Properties of functions and the growth of derivatives of approximating polynomials. (English. Russian original) Zbl 0294.26006 Sov. Math., Dokl. 14, 1281-1285 (1973); translation from Dokl. Akad. Nauk SSSR 212, 19-22 (1973). MSC: 26A15 41A50 42A10 PDFBibTeX XMLCite \textit{V. V. Zhuk} and \textit{G. I. Natanson}, Sov. Math., Dokl. 14, 1281--1285 (1973; Zbl 0294.26006); translation from Dokl. Akad. Nauk SSSR 212, 19--22 (1973)