Journal of applied mathematics & informatics

  • 제42권4호
  • /
  • Pages.867-877
  • /
  • 2024
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

ONE SIDED APPROXIMATION OF UNBOUNDED FUNCTIONS FOR ALGEBRAIC POLYNOMIAL OPERATORS IN WEIGHTED Lp,α-SPACES

  • HAJR IMAD RAJAA (Department of Mathematics, College of Education for Pure Science, University of Anbar) ;
  • ALAA ADNAN AUAD (Department of Mathematics, College of Education for Pure Science, University of Anbar)
  • 투고 : 2023.10.05
  • 심사 : 2024.03.06
  • 발행 : 2024.07.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The objective of this article is to acquire analogs for the degree of best one-sided approximation to investigate some Jackson's well-known theorems for best one-sided approximations in weighted Lp,α-spaces. In addition, some operators that are used to approximate unbounded functions have been introduced as be algebraic polynomials in the same weighted spaces. Our main results are given in terms of degree of the best one-sided approximation in terms of averaged modulus of smoothness.

키워드

참고문헌

  1. J.A. Adell, J. Bustamante, and J.M. Quesada, Polynomial operators for one-sided l p-approximation to riemann integrable functions, J. Inequal. Appl. 2014 (2014), 1-8.
  2. A. Andreev, V.A. Popov, and B. Sendov, Some problems connected with approximation by spline functions and polynomials, Stud. Sci. Math. Hung. 5 (1970), 161-171.
  3. A.A. Auad and F.AL-Sharqi, Identical theorem of approximation unbounded by linear operators, J. Appl. Math. & Inform. 41 (2023), 801-810.
  4. A.A. Auad, M.A. Hilal, and N.S. Khalaf, Best approximation of unbounded functions by modulus of smoothness, Eur. J. Pure Appl. Math. 16 (2023), 944-952.
  5. A.A. Auad and A.A. Hussein, Best simultaneous approximation in weighted space, J. Phys. Conf. Ser. 1234 (2019), 012111.
  6. Alaa Adnan Auad and Mohammed Hamad Fayyadh, The direct and converse theorems for best approximation of algebraic polynomial in lp, α (x), J. Phys. Conf. Ser. 1879 (2021), 032010.
  7. Vladislav Fedorovich Babenko and A.A. Ligun, The order of the best one-sided approximation by polynomials and splines in the l p-metric, Mathematical notes of the Academy of Sciences of the USSR 19 (1976), 194-198.
  8. Z.A. Chanturiya, The modulus of variation of a function and its application in the theory of fourier series, Dokl. Akad. Nauk. 214 (1974), 63-66.
  9. E.P. Dolzhenko and E.A. Sevast'yanov, Approximations of functions in the hausdorff metric by piecewise monotonic (in particular, rational) functions, Mat. Sb. 143 (1976), 508-541.
  10. G. Freud, Uber einseitige approximation durch polynome i, Acta Sci. Math. 16 (1955), 12-28.
  11. T. Ganelius, On one-sided approximation by trigonometrical polynomials, Math. Scand. 4 (1956), 247-258.
  12. L.A. Husain, Unbounded function approximation in some, p l α spaces, M.sc thesis, Al-Mustansirya University, Baghdad, Iraq, 2010.
  13. R. Li and Y. Liu, The best m-term one-sided approximation of besov classes by the trigonometric polynomials, Adv. Pure Appl. Math. 2 (2012), 183.
  14. O. Maizlish, One-sided weighted approximation, Msc. thesis, University of Manitoba, Winnipeg, Canada, 2008.
  15. V.P. Motornyi and A.N. Pas ko, On the best one-sided approximation of some classes of differentiable functions in l˜ 1, East J. Approx. 10 (2004), 159.