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Abstract
In this paper, we investigate the problem of the deviation of a function from its de la Vallée-Poussin sums of Fourier series in Morrey spaces defined on the unite circle in terms of the best approximation to . Moreover, approximation properties of de la Vallée-Poussin sums of Faber series in Morrey-Smirnov classes of analytic functions, defined on a simply connected domain bounded by a curve satisfying Dini's smoothness condition are obtained.
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References
- Guven, A. Trignometric approximation of function in weighted Lp spaces. Sarajevo Journal of Math, 2009, 5(17), 99-108.
- Andersson, J. On the degree of polynomial approximation in Ep(D). Journal of Approximation Theory, 1977, 19(1), 61-68.
- Çavu, A. and Israfilov, D. Approximation by Faber-Laurent rational functions in the mean of functions of class Lp(Γ) with 1< p<+∞. Approximation Theory and its Applications, 1995, 11(1), 105-118.
- Israfilov, D. Approximation by p-Faber-Laurent rational functions. Czechoslovak Mathematical Journal, 2004, 54(129), 751-765.
- Jafarov, S. Approximation by polynomials and rational functions in Orlicz spaces. Journal of computational analysis and applications, 2011, 13(5), 953-962.
- Jafarov, S. On approximation in weighted Smirnov Orlicz classes. Complex Variables and Elliptic Equations, 2012, 57(5), 567-577.
- Israfilov, D. and Akgun, R. Approximation in weighted Smirnov- Orlicz classes. Journal of Math. Kyoto University., 2006, 46(4), 755-770.
- Morrey, C. On the solutions of quasi-linear elliptic partial differential equations. Transactions of the American Mathematical Society, 1938, 43(1), 126-166.
- Israfilov, D. and Tozman, N. Approximation by polynomials in Morrey-Smirnov classes. East Journal on, Approximation, 2008, 14(3), 225-269.
- Israfilov, D. and Tozman, N. Approximation in Morrey-Smirnov classes. Azerbaijan Journal of Math., 2011, 1(1), 99-113.
- Bilalov, B. and Quliyeva, A. On basicity of exponential systems in Morrey-type spaces. International Journal of Mathematics, 2014, 25(06), 1450054 (10 pages).
- Sadigova, S. On approximation by Shift Operators in Morrey Type Spaces. Caspian Journal of Applied Mathematics, Ecology and Economics, 2015, 3(2).
- Bilalov, B., Gasymov, T., and Guliyeva, A. On the solvability of the Riemann boundary value problem in Morrey-Hardy classes. Turkish Journal of Mathematics, 2016, 40(5), 1085-1101.
- Guliyeva, F., Abdullayeva, R., and Cetin, S. On Morrey type Spaces and Some Properties. Caspian Journal of Applied Mathematics, Ecology and Economics, 2016, 4(1), 3-16.
- Kokilasvili, V. On approximation of analytic functions from Ep classes. Trudy Tbiliss. Razmadze Mathematical Institute, 1968, 34, 82-102.
- Guven, A. and Israfilov, D. Approximation by mean of Fourier trignometric series in weighted Orlicz spaces. Advanced Studies in Contemporary Mathematics, 2009, 19(2), 283-295.
- Jafarov, S. Approximation of functions by de la Vallee-Poussin sums in weighted Orlicz spaces. Arabian Journal of Mathematics, 2016, 5(3), 125-137.
- Fucík, S., John, O., Kufner, A., and Pick, L. Function spaces: De Gruyter Series in Nonlinear Analysis and Applications 14 (2nd Edition), De Gruyter, Berlin/Boston, 2013.
- Devore, R.A. and Lorentz, G.G. Constructive approximation: A Series of Comprehensive Studies in Mathematics, Springer, New York, 1993.
- Pommerenke, C. Boundary Behavior of Conformal Maps: A Series of Comprehensive Studies in Mathematics, Springer, Berlin, 1992.
- Warschawski, S.E. Uber das ranverhalten der Ableitung der Abildunggsfunktion bei Konfermer Abbildung, Math. Z. 1932, 35(German).
- Markushevich, A. Theory of Analytic Functions, Izdatelstvo Nauka, Moscow, 1968.
- Duren, P.L. Theory of Hp spaces: A Series of Monographs and Textbooks, Academic Press, New York, 1970.
References
Guven, A. Trignometric approximation of function in weighted Lp spaces. Sarajevo Journal of Math, 2009, 5(17), 99-108.
Andersson, J. On the degree of polynomial approximation in Ep(D). Journal of Approximation Theory, 1977, 19(1), 61-68.
Çavu, A. and Israfilov, D. Approximation by Faber-Laurent rational functions in the mean of functions of class Lp(Γ) with 1< p<+∞. Approximation Theory and its Applications, 1995, 11(1), 105-118.
Israfilov, D. Approximation by p-Faber-Laurent rational functions. Czechoslovak Mathematical Journal, 2004, 54(129), 751-765.
Jafarov, S. Approximation by polynomials and rational functions in Orlicz spaces. Journal of computational analysis and applications, 2011, 13(5), 953-962.
Jafarov, S. On approximation in weighted Smirnov Orlicz classes. Complex Variables and Elliptic Equations, 2012, 57(5), 567-577.
Israfilov, D. and Akgun, R. Approximation in weighted Smirnov- Orlicz classes. Journal of Math. Kyoto University., 2006, 46(4), 755-770.
Morrey, C. On the solutions of quasi-linear elliptic partial differential equations. Transactions of the American Mathematical Society, 1938, 43(1), 126-166.
Israfilov, D. and Tozman, N. Approximation by polynomials in Morrey-Smirnov classes. East Journal on, Approximation, 2008, 14(3), 225-269.
Israfilov, D. and Tozman, N. Approximation in Morrey-Smirnov classes. Azerbaijan Journal of Math., 2011, 1(1), 99-113.
Bilalov, B. and Quliyeva, A. On basicity of exponential systems in Morrey-type spaces. International Journal of Mathematics, 2014, 25(06), 1450054 (10 pages).
Sadigova, S. On approximation by Shift Operators in Morrey Type Spaces. Caspian Journal of Applied Mathematics, Ecology and Economics, 2015, 3(2).
Bilalov, B., Gasymov, T., and Guliyeva, A. On the solvability of the Riemann boundary value problem in Morrey-Hardy classes. Turkish Journal of Mathematics, 2016, 40(5), 1085-1101.
Guliyeva, F., Abdullayeva, R., and Cetin, S. On Morrey type Spaces and Some Properties. Caspian Journal of Applied Mathematics, Ecology and Economics, 2016, 4(1), 3-16.
Kokilasvili, V. On approximation of analytic functions from Ep classes. Trudy Tbiliss. Razmadze Mathematical Institute, 1968, 34, 82-102.
Guven, A. and Israfilov, D. Approximation by mean of Fourier trignometric series in weighted Orlicz spaces. Advanced Studies in Contemporary Mathematics, 2009, 19(2), 283-295.
Jafarov, S. Approximation of functions by de la Vallee-Poussin sums in weighted Orlicz spaces. Arabian Journal of Mathematics, 2016, 5(3), 125-137.
Fucík, S., John, O., Kufner, A., and Pick, L. Function spaces: De Gruyter Series in Nonlinear Analysis and Applications 14 (2nd Edition), De Gruyter, Berlin/Boston, 2013.
Devore, R.A. and Lorentz, G.G. Constructive approximation: A Series of Comprehensive Studies in Mathematics, Springer, New York, 1993.
Pommerenke, C. Boundary Behavior of Conformal Maps: A Series of Comprehensive Studies in Mathematics, Springer, Berlin, 1992.
Warschawski, S.E. Uber das ranverhalten der Ableitung der Abildunggsfunktion bei Konfermer Abbildung, Math. Z. 1932, 35(German).
Markushevich, A. Theory of Analytic Functions, Izdatelstvo Nauka, Moscow, 1968.
Duren, P.L. Theory of Hp spaces: A Series of Monographs and Textbooks, Academic Press, New York, 1970.