Direct estimates of the rate of approximation by the Kantorovich operator in variable exponent Lebesgue spaces. (English) Zbl 1543.41004
Reviewer: Fahreddin Abdullayev (Mersin)
Found 180 Documents (Results 1–100)
Multivariate fuzzy approximation by neural network operators activated by a general sigmoid function. (English) Zbl 1537.41008
Order of approximation for exponential sampling type neural network operators. (English) Zbl 1514.41008
Reviewer: Mohammed El Aïdi (Bogotá)
Direct and inverse approximation theorems in the Besicovitch-Musielak-Orlicz spaces of almost periodic functions. (English) Zbl 1516.42005
Ukr. Math. J. 74, No. 5, 801-819 (2022) and Ukr. Mat. Zh. 74, No. 5, 701-716 (2022).
Reviewer: Bogdan Szal (Zielona Góra)
Multivariate fuzzy approximation by neural network operators activated by several Sigmoid functions revisited. (English) Zbl 1516.26021
A strong converse inequality for generalized sampling operators. (English) Zbl 1504.41014
Reviewer: Vijay Gupta (New Delhi)
Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces. (English) Zbl 1485.42010
Reviewer: Luis Filipe Pinheiro de Castro (Aveiro)
Jackson-type inequalities and widths of functional classes in the Musielak-Orlicz type spaces. (English) Zbl 1477.41004
Reviewer: D. K. Ugulava (Tbilisi)
Generalized characteristics of smoothness and some extreme problems of the approximation theory of functions in the space \(L_2(\mathbb{R})\). I. (English. Russian original) Zbl 1428.41015
Ukr. Math. J. 70, No. 9, 1345-1374 (2019); translation from Ukr. Mat. Zh. 70, No. 9, 1166-1191 (2018).
Reviewer: Stefan Cobzaş (Cluj-Napoca)
Quantitative approximation by perturbed Kantorovich-Choquet neural network operators. (English) Zbl 1416.41016
Fourier-Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in \(L_2\) metric: Jackson’s type direct theorems. (English) Zbl 1407.33015
Approximation by shift invariant multivariate sublinear-Shilkret operators. (English) Zbl 1414.41012
Optimal order Jackson type inequality for scaled Shepard approximation. (English) Zbl 1384.41009
Reviewer: Yuri A. Farkov (Moscow)
On the moduli of continuity and fractional-order derivatives in the problems of best mean-square approximation by entire functions of the exponential type on the entire real axis. (English. Russian original) Zbl 1499.41038
Ukr. Math. J. 69, No. 5, 696-724 (2017); translation from Ukr. Mat. Zh. 69, No. 5, 599-623 (2017).
Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). III. (English. Russian original) Zbl 1490.41015
Ukr. Math. J. 68, No. 10, 1495-1518 (2017); translation from Ukr. Mat. Zh. 68, No. 10, 1299-1319 (2016).
Trigonometric polynomial approximation, \(K\)-functionals and generalized moduli of smoothness. (English. Russian original) Zbl 1368.42007
Sb. Math. 208, No. 2, 237-254 (2017); translation from Mat. Sb. 208, No. 2, 70-87 (2017).
Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). I. (English. Russian original) Zbl 1498.41011
Ukr. Math. J. 68, No. 6, 823-848 (2016); translation from Ukr. Mat. Zh. 68, No. 6, 723-745 (2016).
MSC:
41A17
On the application of linear positive operators for approximation of functions. (English. Russian original) Zbl 1360.41012
Math. Notes 100, No. 5, 666-676 (2016); translation from Mat. Zametki 100, No. 5, 689-700 (2016).
Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions. (English. Russian original) Zbl 1342.41033
Math. Notes 99, No. 2, 222-242 (2016); translation from Mat. Zametki 99, No. 2, 215-238 (2016).
Intelligent systems II. Complete approximation by neural network operators. (English) Zbl 1325.68008
Studies in Computational Intelligence 608. Cham: Springer (ISBN 978-3-319-20504-5/hbk; 978-3-319-20505-2/ebook). xv, 712 p. (2016).
Reviewer: Claudia Simionescu-Badea (Wien)
High order multivariate fuzzy approximation by neural network operators based on the error function. (English) Zbl 1371.41031
Multivariate fuzzy-random error function based neural network approximation. (English) Zbl 1371.41030
Generalized smoothness characteristics in Jackson-type inequalities and widths of classes of functions in \(L_2\). (English. Russian original) Zbl 1339.41017
Math. Notes 98, No. 4, 572-588 (2015); translation from Mat. Zametki 98, No. 4, 511-529 (2015).
Jackson-type inequalities for spherical neural networks with doubling weights. (English) Zbl 1326.41019
Quality of approximation by Fourier means in terms of general moduli of smoothness. (English. Russian original) Zbl 1325.41006
Math. Notes 98, No. 1, 3-10 (2015); translation from Mat. Zametki 98, No. 1, 3-11 (2015).
Moduli of smoothness related to the Laplace-operator. (English) Zbl 1329.42002
Reviewer: Delfina Roux (Milano)
New moduli of smoothness: weighted DT moduli revisited and applied. (English) Zbl 1329.41020
Reviewer: Radu Păltănea (Braşov)
Structural characteristics of functions from \(L_2\) and the exact values of widths of some functional classes. (English. Ukrainian original) Zbl 1323.41015
J. Math. Sci., New York 206, No. 1, 97-114 (2015); translation from Ukr. Mat. Visn. 11, No. 3, 417-441 (2014).
Bernstein-Jackson-type inequalities and Besov spaces associated with unbounded operators. (English) Zbl 1370.47014
Multivariate fuzzy-random quasi-interpolation neural network approximation operators. (English) Zbl 1373.62479
Higher order multivariate fuzzy approximation by basic neural network operators. (English. Spanish summary) Zbl 1329.26051
On window methods in generalized Shannon sampling operators. (English) Zbl 1318.42002
Zayed, Ahmed I. (ed.) et al., New perspectives on approximation and sampling theory. Festschrift in honor of Paul Butzer’s 85th birthday. Cham: Birkhäuser/Springer (ISBN 978-3-319-08800-6/hbk; 978-3-319-08801-3/ebook). Applied and Numerical Harmonic Analysis, 63-85 (2014).
Reviewer: Sorin Gheorghe Gal (Oradea)
Wavelet expansions on the Cantor group. (English. Russian original) Zbl 1315.42023
Math. Notes 96, No. 5, 996-1007 (2014); translation from Mat. Zametki 96, No. 6, 926-938 (2014).
Reviewer: Manfred Tasche (Rostock)
Sharp estimates of integrals in terms of the second modulus of continuity. (English. Russian original) Zbl 1314.41019
Math. Notes 96, No. 4, 465-476 (2014); translation from Mat. Zametki 96, No. 4, 483-495 (2014).
A direct theorem of approximation theory for a general modulus of smoothness. (English. Russian original) Zbl 1314.41009
Math. Notes 95, No. 6, 833-842 (2014); translation from Mat. Zametki 95, No. 6, 899-910 (2014).
Multivariate fuzzy-random normalized neural network approximation operators. (English) Zbl 1302.60013
Rate of convergence of some neural network operators to the unit-univariate case, revisited. (English) Zbl 1299.41025
Reviewer: Marija Stanić (Kragujevac)
MSC:
41A25
On some extremal problems of approximation theory of functions on the real axis. I. (English. Russian original) Zbl 1268.41023
J. Math. Sci., New York 188, No. 2, 146-166 (2013); translation from Ukr. Mat. Visn. 9, No. 3, 401-429 (2012).
Best mean-square approximation of functions defined on the real axis by entire functions of exponential type. (English. Russian original) Zbl 1259.41042
Ukr. Math. J. 64, No. 5, 680-692 (2012); translation from Ukr. Mat. Zh. 64, No. 5, 604-615 (2012).
The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus. (English. Russian original) Zbl 1303.41007
J. Math. Sci., New York 178, No. 2, 132-143 (2011); translation from Zap. Nauchn. Semin. POMI 383, 33-52 (2010).
Higher order multivariate fuzzy approximation by multivariate fuzzy wavelet type and neural network operators. (English) Zbl 1228.42037
MSC:
42C40
Classes of functions with improved estimates in approximation by the max-product Bernstein operator. (English) Zbl 1226.41007
Multivariate sigmoidal neural network approximation. (English) Zbl 1228.65018
Reviewer: Aurelian Bejancu (Safat)
Intelligent systems. Approximation by artificial neural networks. (English) Zbl 1243.68002
Intelligent Systems Reference Library 19. Berlin: Springer (ISBN 978-3-642-21430-1/hbk; 978-3-642-21431-8/ebook). v, 107 p. (2011).
Reviewer: Claudia Simionescu-Badea (Wien)
Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes. (Russian, English) Zbl 1240.30187
Ukr. Mat. Zh. 62, No. 8, 1032-1043 (2010); translation in Ukr. Math. J. 62, No. 8, 1199-1212 (2010).
Trigonometric approximation of \(\mathrm{SO}(N)\) loops. (English) Zbl 1206.41013
Reviewer: Francisco Pérez Acosta (La Laguna)
Uniform real and fuzzy estimates for distances between wavelet type operators at real and fuzzy setting. (English) Zbl 1197.26049
Exact constants in Jackson-type inequalities for \(L_2\)-approximation on an axis. (Russian, English) Zbl 1224.41045
Ukr. Mat. Zh. 61, No. 1, 92-98 (2009); translation in Ukr. Math. J. 61, No. 1, 112-120 (2009).
Counterexample in comonotone approximation of periodic functions. (Ukrainian) Zbl 1199.41063
MSC:
41A17
On Jackson type inequalities and width of classes of periodical functions in the space \(L_2\). (Russian) Zbl 1199.41068
MSC:
41A17
On the best \(L_2\)-approximations of functions by using wavelets. (Russian, English) Zbl 1164.41320
Ukr. Mat. Zh. 60, No. 8, 1119-1127 (2008); translation in Ukr. Math. J. 60, No. 8, 1307-1317 (2008).
MSC:
41A17
Sharp Jackson inequalities. (English) Zbl 1136.41003
Reviewer: Shun Sheng Guo (Shijiazhuang)
Jackson and Bernstein theorems for the weight \(\exp(-|x|)\) on \(\mathbb R\). (English) Zbl 1151.41009
Reviewer: Dan Bārbosu (Baia Mare)
MSC:
41A17
Quadratic stable wavelet bases on general meshes. (English) Zbl 1099.42029
Reviewer: Manfred Tasche (Rostock)
Jackson type inequalities in approximation of functions from the \(S^p\) space by the Voronoi method. (Ukrainian) Zbl 1199.41069
MSC:
41A17
Holomorphic Jackson’s theorems in polydiscs. (English) Zbl 1070.41007
Reviewer: Alexander Tovstolis (Donetsk)
Direct approximation theorems for Dirichlet series in the norm of uniform convergence. (English) Zbl 1062.30006
Reviewer: Elena E. Berdysheva (Stuttgart)
Interpolatory type estimates in copositive approximation. (English) Zbl 1113.41020
Reviewer: Todor Boyanov (Sofia)
MSC:
41A17
Exact constant in an inequality of Jackson type for \(L_2\)-approximation on the line and exact values of mean widths of functional classes. (English) Zbl 1113.41021
Reviewer: S. B. Vakarchuk
Inequalities of Jackson type and exact values of widths of classes of functions in the spaces \(S^p,1\leq p<\infty\). (Russian, English) Zbl 1127.42302
Ukr. Mat. Zh. 56, No. 5, 595-605 (2004); translation in Ukr. Math. J. 56, No. 5, 718-729 (2004).
Negative results in form-preserving approximation of higher order. (English. Russian original) Zbl 1114.41006
Math. Notes 76, No. 6, 758-769 (2004); translation from Mat. Zametki 76, No. 6, 812-823 (2004).
Reviewer: Ganesh Datta Dikshit (Auckland)
High-order fuzzy approximation by fuzzy wavelet type and neural network operators. (English) Zbl 1071.41020
High-order approximation by multivariate shift-invariant convolution type operators. (English) Zbl 1071.41019
Combinations of multivariate averages. (English) Zbl 1109.41010
Reviewer: Alexander Tovstolis (Donetsk)
A Kolmogorov-type inequality. (English) Zbl 1063.26009
Reviewer: Petr Gurka (Praha)
Jackson-type inequalities in the space \(S^p\). (Ukrainian, English) Zbl 1089.41007
Ukr. Mat. Zh. 55, No. 9, 1167-1177 (2003); translation in Ukr. Math. J. 55, No. 9, 1410-1422 (2003).
Operators generated by a quasi-scaling type function. (English) Zbl 1079.41013
Reviewer: Dan Bārbosu (Baia Mare)
MSC:
41A25
Jackson-type estimate in monotone approximation by bivariate polynomials. (English) Zbl 1063.41010
Reviewer: Eleonora A. Storozhenko (Odessa)
High order approximation by univariate shift-invariant integral operators. (English) Zbl 1046.41013
Agarwal, Ravi P. (ed.) et al., Nonlinear analysis and applications: To V. Lakshmikantham on his 80th birthday. Vol. 1. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1711-1/hbk). 141-164 (2003).
Reviewer: Boris I. Golubov (Dolgoprudny)
Multivariate simultaneous approximation. (English) Zbl 1025.41002
Reviewer: Shi Ying-Guang (Beijing)
Jackson’s theorem for compact groups. (English) Zbl 1020.43004
Reviewer: S.Platonov (Petrozavodsk)
Approximation with interpolatory constraints. (English) Zbl 0993.41005
Reviewer: S.M.Mazhar (Kuwait)
Minimization of exact constants in Jackson type inequalities and diameters of functions belonging to \(L_2[0,2\pi]\). (Russian. English summary) Zbl 1049.42001
Reviewer: Alexander E. Guterman (Moskva)
Inequalities for some iterated linear operators and their applications in approximation theory. (English) Zbl 1027.41020
On the best polynomial approximations in \(L_2\) of some classes of \(2\pi\)-periodic functions and of the exact values of their \(n\)-widths. (English. Russian original) Zbl 1018.41016
Math. Notes 70, No. 3, 300-310 (2001); translation from Mat. Zametki 70, No. 3, 334-345 (2001).
Realization and smoothness related to the Laplacian. (English) Zbl 0997.42002
Reviewer: W.Pleśniak (Kraków)
Best approximation by Vilenkin-like systems. (English) Zbl 0992.42011
Reviewer: L.Leindler (Szeged)
On Jackson type inequality in Orlicz classes. (English) Zbl 1004.42002
Reviewer: Eleonora Storozhenko (Odessa)
Jackson-type theorems for compact symmetric spaces of rank 1. (Russian, English) Zbl 0977.41016
Sib. Mat. Zh. 42, No. 1, 136-148 (2001); translation in Sib. Math. J. 42, No. 1, 119-130 (2001).
Reviewer: V.Grebenev (Novosibirsk)
Convex pointwise polynomial approximation. (English. English summary) Zbl 1028.41012
Kovtunets, V. V. (ed.), Approximation theory and its applications. Proceedings of the international conference dedicated to the memory of Vladislav Kirillovich Dzyadyk held in Kiev, Ukraine, May 27-31, 1999. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 31, 337-343 (2000).
Reviewer: A.M.Gomilko (Kyïv)
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