References

APPROXIMATION THEOREMS IN WEIGHTED ORLICZ SPACES


[1] R. Akgun and D. M. Israfilov, Approximation and moduli of fractional order in Smirnov-Orlicz classes, Glasnik Matematicki 43 (2008), 121-136.

[2] R. Akgun, Sharp Jackson and converse theorems of trigonometric approximation in weighted Lebesgue spaces, Proc. A. Razmadze Math. Inst. 152 (2010), 1-18.

[3] R. Akgun and D. M. Israfilov, Approximation of weighted Orlicz spaces, Math. Slovaca 61(4) (2011), 601-618.

[4] R. A. De Vore and G. G. Lorentz, Constructive Approximation, Springer, 1993.

[5] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer Ser. Comput. Math. 9, Springer, New York, 1987.

[6] W. Garidi, On approximation by polynomials in Orlicz spaces, Approx. Theory Appl. (N.S.) 7 (1991), 97-110.

[7] I. Genebashvili, A. Gogatishvili, V. Kokilashvili and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Longman, 1998.

[8] E. A. Haciyeva, Investigation of the Properties of Functions with Quasimonotone Fourier Coefficients in Generalized Nikolskii-Besov Spaces, Author’s Summary of Dissertation, Tbilisi, 1986 (Russian).

[9] D. M. Israfilov and R. Akgun, Approximation in weighted Smirnov-Orlicz classes, J. Math. Kyoto Univ. 46 (2006), 755-770.

[10] V. M. Kokilashvili, On analytic functions of Smirnov-Orlicz spaces, Studia Math. 31 (1968), 43-59.

[11] V. M. Kokilashvili, A direct theorem on mean approximation of analytic functions by polynomials, Dokl. Akad. Nauk SSSR 10 (1969), 411-414.

[12] V. M. Kokilashvili, A note on extrapolation and modular inequalities, Proc. A. Razmadze Math. Inst. 150 (2009), 91-97.

[13] M. A. Krasnosel’skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Noordholf, 1961.

[14] N. X. Ky, On approximation by trigonometric polynomials in Studia Sci. Math. Hungar. 28 (1993), 183-188.

[15] H. N. Mhaskar, Introduction to the Theory Weighted Polynomial Approximation, Series in Approximation and Decompositions, 7 World Sci., River Edge, NJ, 1996.

[16] V. G. Ponomarenko, Approximation of periodic functions in Orlicz spaces, Translated from Sibirskii Matematicheskii Zhurnal 7(6) (1966), 1337-1346.

[17] A. R.-K. Ramazanov, On approximation by polynomials and rational functions in Orlicz spaces, Anal. Math. 10 (1984), 117-132.

[18] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.

[19] M. M. Rao and Z. D. Ren, Application of Orlicz Spaces, Dekker, 2002.

[20] K. Runovski, On Jackson type inequality in Orlicz classes, Rev. Mat. Comput. 14 (2001), 395-404.

[21] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, 1993.

[22] A. F. Timan, Theory of Approximation of Functions of a Real Variable, International Series of Monographs on Pure and Applied Mathematics 3, Pergamon Press and Macmillan, Oxford, 1963.

[23] Y. E. Yildirir and D. M. Israfilov, The properties of convolution type transforms in weighted Orlicz spaces, Glasnik Matematicki 45 (2010), 461-474.

[24] A. Zygmund, Trigonometric Series, 2nd Edition, Vols. I, II, Cambridge University Press, New York, 1959.