Simultaneous approximation by polynomials in Orlicz spaces generated by quasiconvex Young functions

Authors

  • huseyin koc Balikesir University/Institute of Science

Keywords:

Moduli of smoothness, Orlicz spaces, simultaneous approximations, trigonometric/algebraic approximation.

Abstract

In this paper we prove some theorems on simultaneous approximation by trigonometric or algebraic polynomials in Orlicz spaces constructed by Young functions belonging to a reasonably wide class.

References

Akgn, R. (2011). Inequalities for one sided approximation in Orlicz

spaces. Hacettepe Journal of Mathematics and Statistics, 40(2):231-

Akgn, R. & Israfilov, D.M. (2011). Approximation in weighted

Orlicz spaces. Mathematica Slovaca, 61(4):601-618.

Akgn, R. (2012). Approximating polynomials for functions of

weighted Smirnov-Orlicz spaces. Journal of Function Spaces and

Applications, Article ID 982360: Pp. 41.

Akgn, R. & Ko, H. (2012). Approximation by interpolating

polynomials in weighted symmetric Smirnov spaces. Hacettepe Journal

of Mathematics and Statistics, 41(5):643-649.

Akgn, R. (2016). Some inequalities of trigonometric approximation

in weighted Orlicz spaces. Mathematica Slovaca, 66(1):217-234.

Akgn, R. & Ko, H. (2016). Simultaneous approximation of functions

in Orlicz spaces with Muckenhoupt weights, Complex Variables and

Eliptic Equations, 61(8):1107-1115.

Chen, Yung-ming. (1964). On two-functional spaces. Studia

Mathematica, 24:61-88.

Cohen, E. 1978. On the degree of approximation of a function by

the partial sums of its Fourier series. Transactions of the American

Mathematical Society, 235:35-74.

Garidi, Wu. (1991). On approximation by polynomials in Orlicz

spaces. Approximation Theory and Applications, 7(3):97-110.

Israfilov, D.M. & Akgn, R. (2010). Simultaneous and converse

approximation theorems in weighted Orlicz spaces. Bulletin of the

Belgian Mathematical Society, Simon Stevin, 17(1):13-28.

Krasnoselski?, M.A. & Ruticki?, Y.B. (1961). Convex functions and

Orlicz spaces. Translated from the first Russian edition by Leo F. Boron,

P. Noordhoff Ltd., Groningen.

Kokilavili, V.M. (1965). An inverse theorem of the constructive theory

of functions in Orlicz spaces. (Russian) Soob?. Akad. Nauk Gruzin.

SSR, 37:263-270.

Lorentz, G.G. (1966). Approximation of functions. Holt, Rinehart and

Winston.

Ponomarenko, V.G. (1966). Approximation of periodic functions in

an Orlicz space. (Russian) Sibirskii Matematicheskii Zhurnal, 7:1337-

Ramazanov, A.R.K. (1984). On approximation by polynomials and

rational functions in Orlicz spaces. Analysis Mathematica, 10(2):117-

Tsyganok, I.I. (1966). A generalization of a theorem of Jackson.

(Russian) Matematicheskii Sbornik, 71(113):257-260.

Yiqun, Yang. (1984.) K-functional and degree of approximation (I). (in

Chinese), Acta Mathematica Sinica, 27(1):133-144.

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Published

17-11-2016