Vasylyk, V. B.; Sytnyk, D. O.; Komashchenko, N. O. Method without accuracy saturation of solution of nonlocal multipoint problem for first-order evolutionary differential equation in Banach space. (Ukrainian. English summary) Zbl 1474.65150 Zb. Pr. Inst. Mat. NAN Ukr. 16, No. 2, 7-15 (2019). MSC: 65J08 34G10 34B10 PDFBibTeX XMLCite \textit{V. B. Vasylyk} et al., Zb. Pr. Inst. Mat. NAN Ukr. 16, No. 2, 7--15 (2019; Zbl 1474.65150) Full Text: Link
Shvaĭ, K. V. Estimates of the best orthogonal trigonometric approximations of the generalized multidimensional analogues of the Bernoulli kernels and classes \(L_{\beta,1}^{\psi}\) in the space \(L_q\). (Ukrainian. English summary) Zbl 1374.42009 Zb. Pr. Inst. Mat. NAN Ukr. 13, No. 1, 300-320 (2016). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{K. V. Shvaĭ}, Zb. Pr. Inst. Mat. NAN Ukr. 13, No. 1, 300--320 (2016; Zbl 1374.42009)
Shkapa, V. V. Greedy algorithms of classes \((\psi,\beta)\)-differentiable periodic functions. (Ukrainian. English summary) Zbl 1340.41045 Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 299-312 (2015). MSC: 41A50 42A10 PDFBibTeX XMLCite \textit{V. V. Shkapa}, Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 299--312 (2015; Zbl 1340.41045)
Shevchenko, I. A. On best non-symmetric \(L_1\)-approximations of some classes of convolutions with generalized splines. (Russian. English summary) Zbl 1340.41008 Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 290-298 (2015). MSC: 41A15 41A50 PDFBibTeX XMLCite \textit{I. A. Shevchenko}, Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 290--298 (2015; Zbl 1340.41008)
Romanyuk, V. S. Nonlinear approximation in spaces of multiple sequences. (Russian. English summary) Zbl 1340.42004 Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 253-261 (2015). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{V. S. Romanyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 253--261 (2015; Zbl 1340.42004)
Shkapa, V. V. Best approximations of analogues of the Bernoulli kernels and classes of \((\psi, \beta)\)-differentiable periodic functions. (Ukrainian. English summary) Zbl 1340.41050 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 413-424 (2014). MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{V. V. Shkapa}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 413--424 (2014; Zbl 1340.41050)
Shydlich, A. L.; Chaĭchenko, S. O. Approximate characteristics of diagonal operators in spaces \(\ell_p\). (Ukrainian. English summary) Zbl 1340.41051 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 399-412 (2014). MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{A. L. Shydlich} and \textit{S. O. Chaĭchenko}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 399--412 (2014; Zbl 1340.41051)
Yanchenko, S. Ya. Order estimates for approximative characteristics of functions from generalized classes of mixed smoothness of the Nikol’skii-Besov type. (Ukrainian. English summary) Zbl 1313.42022 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 330-343 (2014). MSC: 42A10 41A50 30E10 PDFBibTeX XMLCite \textit{S. Ya. Yanchenko}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 330--343 (2014; Zbl 1313.42022)
Shkapa, V. V. Best orthogonal trigonometric approximations of functions from classes \(L^{\psi}_{\beta, 1}\). (Ukrainian. English summary) Zbl 1313.41060 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 315-329 (2014). MSC: 41A50 42A10 PDFBibTeX XMLCite \textit{V. V. Shkapa}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 315--329 (2014; Zbl 1313.41060)
Shydlich, A. L. Order estimates of functionals in terms of which the best \(n\)-term approximations of classes \({\mathcal F}_{q,\infty}^{\psi}\) are expressed. (Ukrainian. English summary) Zbl 1313.41061 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 287-314 (2014). MSC: 41A50 PDFBibTeX XMLCite \textit{A. L. Shydlich}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 287--314 (2014; Zbl 1313.41061)
Stepanyuk, T. A. Estimates for the best approximations and approximation by Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics. (Ukrainian. English summary) Zbl 1313.42021 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 241-269 (2014). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{T. A. Stepanyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 241--269 (2014; Zbl 1313.42021) Full Text: arXiv
Stasyuk, S. A. Approximation by step-hyperbolic Fourier sums of classes \(MB_{1,\theta}^{\omega}(\overline{\gamma})\). (Ukrainian. English summary) Zbl 1313.42020 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 228-240 (2014). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{S. A. Stasyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 228--240 (2014; Zbl 1313.42020)
Derev’yanko, I. V. Estimates of linear widths of classes \(H^{\Omega}_{p}\) of periodic functions of several variables in the space \(L_q\). (Ukrainian. English summary) Zbl 1313.41069 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 128-145 (2014). MSC: 41A65 41A50 42A10 PDFBibTeX XMLCite \textit{I. V. Derev'yanko}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 128--145 (2014; Zbl 1313.41069)
Vakarchuk, S. V.; Shvachko, A. V. On the best approximation by “angles” in the mean on the plane \(\mathbb R^2\) with the Chebyshev-Hermite weight. (Russian. English summary) Zbl 1313.41024 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 35-46 (2014). MSC: 41A17 41A10 PDFBibTeX XMLCite \textit{S. V. Vakarchuk} and \textit{A. V. Shvachko}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 35--46 (2014; Zbl 1313.41024)
Bodenchuk, V. V. Lower bounds for Kolmogorov widths in classes of convolutions with Neumann kernel. (Ukrainian. English summary) Zbl 1313.41056 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 7-34 (2014). MSC: 41A50 42A10 41A46 41A15 PDFBibTeX XMLCite \textit{V. V. Bodenchuk}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 7--34 (2014; Zbl 1313.41056) Full Text: arXiv
Shkapa, V. V. Estimates of the best \(m\)-term and orthogonal trigonometric approximations of functions of classes \(L^{\psi}_{\beta, p}\), \(1<p<\infty\) in the uniform metrics. (Ukrainian. English summary) Zbl 1313.41059 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 2, 305-317 (2014). MSC: 41A50 42A10 PDFBibTeX XMLCite \textit{V. V. Shkapa}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 2, 305--317 (2014; Zbl 1313.41059)
Serdyuk, A. S.; Stepanyuk, T. A. Order estimates for the best approximation and approximation by Fourier sums of classes of infinitely differentiable functions. (Ukrainian. English summary) Zbl 1313.42019 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 255-282 (2013). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{T. A. Stepanyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 255--282 (2013; Zbl 1313.42019)
Serdyuk, A. S.; Sokolenko, I. V. Approximation by linear methods of classes of \((\psi,\overline{\beta})\)-differentiable functions. (Ukrainian. English summary) Zbl 1313.42018 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 245-254 (2013). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{I. V. Sokolenko}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 245--254 (2013; Zbl 1313.42018) Full Text: arXiv
Serdyuk, A. S.; Grabova, U. Z. Estimates of uniform approximations by Zygmund sums on classes of convolutions of periodic functions. (Ukrainian. English summary) Zbl 1313.42017 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 222-244 (2013). MSC: 42A10 41A50 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{U. Z. Grabova}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 222--244 (2013; Zbl 1313.42017) Full Text: arXiv
Serdyuk, A. S.; Bodenchuk, V. V. Estimates from below for Kolmogorov widths in classes of Poisson integrals. (Ukrainian. English summary) Zbl 1313.41058 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 204-221 (2013). MSC: 41A50 42A10 41A46 41A15 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{V. V. Bodenchuk}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 204--221 (2013; Zbl 1313.41058)
Ivashchuk, Ya. G. Estimates of convergence of Remez type algorithm for interpolation classes. (Ukrainian. English summary) Zbl 1313.41043 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 126-132 (2013). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{Ya. G. Ivashchuk}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 126--132 (2013; Zbl 1313.41043)
Derev’yanko, I. V. Estimates of orthoprojective widths of the classes \(B^{\Omega}_{p,\theta}\) of periodic functions of several variables in the space \(L_q\). (Ukrainian. English summary) Zbl 1313.41068 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 95-109 (2013). MSC: 41A65 41A50 41A63 PDFBibTeX XMLCite \textit{I. V. Derev'yanko}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 95--109 (2013; Zbl 1313.41068)
Voĭtovych, V. A.; Musienko, A. P. Lebesgue type inequalities for the de la Vallée Poussin sums and their interpolation analogues on classes of \((\psi,\overline{\beta})\)-differentiable functions. (Ukrainian. English summary) Zbl 1313.41047 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 39-58 (2013). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{V. A. Voĭtovych} and \textit{A. P. Musienko}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 39--58 (2013; Zbl 1313.41047) Full Text: arXiv
Vakarchuk, S. V.; Shvachko, A. V. On the approximation in the mean with the Chebyshev-Hermite weight by algebraic polynomials on the real axis. (Ukrainian. English summary) Zbl 1313.41023 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 28-38 (2013). MSC: 41A17 41A10 PDFBibTeX XMLCite \textit{S. V. Vakarchuk} and \textit{A. V. Shvachko}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 28--38 (2013; Zbl 1313.41023)
Pokrovskij, A. V. On existence and uniqueness of polynomial of the best approximation in the mean with a sign-sensitive weight. (Russian. English summary) Zbl 1289.41053 Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 4-5, 496-606 (2013). MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{A. V. Pokrovskij}, Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 4--5, 496--606 (2013; Zbl 1289.41053)
Serdyuk, A. S.; Sokolenko, I. V. Uniform approximations of classes of \(({\psi},\overline{\beta})\)-differentiate functions by linear methods. (Ukrainian. English summary) Zbl 1249.41071 Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 181-189 (2011). MSC: 41A50 42A10 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{I. V. Sokolenko}, Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 181--189 (2011; Zbl 1249.41071)
Musienko, A. P. The Lebesgue type inequalities for the de la Vallée Poussin sums on sets of \(({\psi},{\beta})\)-differentiate functions. (Ukrainian. English summary) Zbl 1249.41041 Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 128-150 (2011). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{A. P. Musienko}, Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 128--150 (2011; Zbl 1249.41041)
Novak, Ya. V. A Kolmogorov type criterion for a partial fraction. (Ukrainian. English summary) Zbl 1240.41078 Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 2, 385-392 (2010). MSC: 41A50 PDFBibTeX XMLCite \textit{Ya. V. Novak}, Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 2, 385--392 (2010; Zbl 1240.41078)
Stasyuk, S. A. Approximation by Fourier sums of the classes \(B^{\Omega}_{1,\theta}\) of periodic functions in the space \(L_1\). (Russian. English summary) Zbl 1240.41080 Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 338-344 (2010). MSC: 41A50 42A10 PDFBibTeX XMLCite \textit{S. A. Stasyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 338--344 (2010; Zbl 1240.41080)
Serdyuk, A. S.; Musienko, A. P. Lebesgue type inequalities for the de la Vallée Poussin sums in approximation of Poisson integrals. (Ukrainian. English summary) Zbl 1240.41045 Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 298-316 (2010). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{A. S. Serdyuk} and \textit{A. P. Musienko}, Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 298--316 (2010; Zbl 1240.41045)
Savchuk, V. V. Properties of reproduction kernels of classes of holomorphic functions and extremal problems of approximation theory. (Ukrainian. English summary) Zbl 1240.41079 Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 235-263 (2010). MSC: 41A50 PDFBibTeX XMLCite \textit{V. V. Savchuk}, Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 235--263 (2010; Zbl 1240.41079)
Gnatyuk, Yu. V.; Gudyma, U. V.; Gnatyuk, V. O. A method of approximation of a compact-valued map on a finite dimensional space with restrictions determined by a system of convex sets. (Ukrainian. English summary) Zbl 1240.41076 Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 21-35 (2010). MSC: 41A50 PDFBibTeX XMLCite \textit{Yu. V. Gnatyuk} et al., Zb. Pr. Inst. Mat. NAN Ukr. 7, No. 1, 21--35 (2010; Zbl 1240.41076)
Stasyuk, S. A.; Yanchenko, S. Ya. Best approximations of the classes \({B}^{\Omega}_{p,\theta}\) of functions of many variables in the space \(L_p(\mathbb R^d)\). (Ukrainian) Zbl 1199.41163 Zb. Pr. Inst. Mat. NAN Ukr. 5, No. 1, 367-384 (2008). MSC: 41A50 PDFBibTeX XMLCite \textit{S. A. Stasyuk} and \textit{S. Ya. Yanchenko}, Zb. Pr. Inst. Mat. NAN Ukr. 5, No. 1, 367--384 (2008; Zbl 1199.41163)
Manzhos, T. V. Characterization of polynomial of the best approximation of function of several variables with restrictions of derivatives. (Ukrainian) Zbl 1199.41156 Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 186-199 (2007). MSC: 41A50 42B05 PDFBibTeX XMLCite \textit{T. V. Manzhos}, Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 186--199 (2007; Zbl 1199.41156)
Kononovych, T. O. Estimate of the best approximation by trigonometric polynomials of functions from the space \(L_p(Q^2),1<p<\infty\), in terms of the Fourier coefficients. (Ukrainian) Zbl 1199.42048 Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 172-185 (2007). MSC: 42B05 41A50 PDFBibTeX XMLCite \textit{T. O. Kononovych}, Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 172--185 (2007; Zbl 1199.42048)
Vakarchuk, S. B.; Shchitov, A. N. Estimates of the best one-sided approximation of some classes of functions by polynomials constructed on Haar system. (Russian) Zbl 1199.41165 Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 7-22 (2007). MSC: 41A50 41A58 PDFBibTeX XMLCite \textit{S. B. Vakarchuk} and \textit{A. N. Shchitov}, Zb. Pr. Inst. Mat. NAN Ukr. 4, No. 1, 7--22 (2007; Zbl 1199.41165)
Stasyuk, S. A. Best approximation of classes \(B_{p,\theta}^{\Omega}(\gamma)\) in metric of the space \(L_q\). (Ukrainian) Zbl 1199.41162 Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 258-267 (2005). MSC: 41A50 41A65 PDFBibTeX XMLCite \textit{S. A. Stasyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 258--267 (2005; Zbl 1199.41162)
Kotsyubyns’ka, T. V. Minimal admissible pairs of sets and their properties. (Ukrainian) Zbl 1199.41155 Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 135-148 (2005). MSC: 41A50 PDFBibTeX XMLCite \textit{T. V. Kotsyubyns'ka}, Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 135--148 (2005; Zbl 1199.41155)
Gudyma, U. V.; Gnatyuk, Yu. V.; Gnatyuk, V. O. On uniqueness of the extreme element and Chebyshev alternance for the problem of the best uniform approximation of continuous compact map. (Ukrainian) Zbl 1199.41166 Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 106-116 (2005). MSC: 41A52 41A30 PDFBibTeX XMLCite \textit{U. V. Gudyma} et al., Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 106--116 (2005; Zbl 1199.41166)
Gudyma, U. V.; Gnatyuk, Yu. V. Conditions of extremality of the element of the best uniform approximation of continuous compact map. (Ukrainian) Zbl 1199.41102 Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 93-105 (2005). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{U. V. Gudyma} and \textit{Yu. V. Gnatyuk}, Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 93--105 (2005; Zbl 1199.41102)
Gudyma, U. V. Duality relations for the problem of the best uniform approximation of continuous compact map. (Ukrainian) Zbl 1199.41101 Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 81-92 (2005). MSC: 41A30 41A50 PDFBibTeX XMLCite \textit{U. V. Gudyma}, Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 81--92 (2005; Zbl 1199.41101)
Stepanets’, O. I.; Sokolenko, I. V. Approximation of Poisson integrals of functions defined on real axis. (Ukrainian. English summary) Zbl 1199.41164 Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 360-374 (2004). MSC: 41A50 PDFBibTeX XMLCite \textit{O. I. Stepanets'} and \textit{I. V. Sokolenko}, Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 360--374 (2004; Zbl 1199.41164)
Kotsyubyns’ka, T. V. Estimates of the value of the best approximation in bounded range of vector-valued functions. (Ukrainian. English summary) Zbl 1199.41029 Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 207-215 (2004). MSC: 41A10 41A50 PDFBibTeX XMLCite \textit{T. V. Kotsyubyns'ka}, Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 207--215 (2004; Zbl 1199.41029)
Golub, A. P. Rational approximation of some elementary and special functions. (Ukrainian. English summary) Zbl 1199.30230 Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 130-143 (2004). MSC: 30E10 41A50 PDFBibTeX XMLCite \textit{A. P. Golub}, Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 130--143 (2004; Zbl 1199.30230)
Gnayuk, Yu. V.; Gudyma, U. V. The problem of best uniform approximation of continuous compact map by finite dimensional subspace of single-valued continuous maps. (Ukrainian. English summary) Zbl 1199.41154 Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 115-129 (2004). MSC: 41A50 PDFBibTeX XMLCite \textit{Yu. V. Gnayuk} and \textit{U. V. Gudyma}, Zb. Pr. Inst. Mat. NAN Ukr. 1, No. 1, 115--129 (2004; Zbl 1199.41154)