On Best Multiplier Approximation of k-Monotone by Trigonometric Polynomial


  • Saheb K. Al-Saidy Department of Communication, College of Engineering, University of Uruk, Baghdad, IRAQ.
  • Hasan W. Maktoof Department of Mathematics, College of Science, Mustansiriyah University, 10052 Baghdad, IRAQ.. https://orcid.org/0000-0002-6759-0629
  • Abdul Khaleq O. Mazeel Department of Mathematics, College of Science, Mustansiriyah University, 10052 Baghdad, IRAQ.
  • Baba Galadima Agaie Department of Mathematics, Faculty of Science, Federal University of Dutse, Nigeria




Multiplier integral, Multiplier averaged modulus of smoothness, Multiplier norm.


The main goal of this paper is to study the degree of the best multiplier approximation of monotone unbounded functions in L_(p,λ_n)-space on the closed interval [-π,π] by means of K-functional, which we represented with, K(f,L_(p,λ_n ),W_(p,λ_n)^1,W ̃_(p,λ_n)^1), defined by the W_(p,λ_n)^1 and W ̃_(p,λ_n)^1  that are referred to during this research. In addition, we have established a set of definitions, concepts and some useful lemmas that are needed in our work.


Download data is not yet available.


A. Güven and D. M. İsrafilov, "Trigonometric approximation in generalized Lebesgue spaces L_p (x)," Journal of Mathematical Inequalities, vol. 4, no. 285-299, 2010.


H. A. Kadhim, "On best Trigonometric approximation in L_p (μ)- space," Dep. of Math. Journal of Education College of computer and Math. University of Thi-Qar, vol. 3, no. 2, 2012.

S. Al-Saidy and H. Z. Ali, "Best multiplier approximation of periodic unbounded functions using trigonometric operators," PhD. Thesis, University of Al-Mustansiriya, College of Science, Department, 2020.

S. K. Jassim, Al-Jawari, N. J. and Hassan R. F., "The Best One-Sided Multiplier Approximation," PhD. Thesis, Al-Mustansiriya University, College of Science, Department of Mathematics, 2022.

G. H. Hardy, Divergent Series, First Ed. ed. At the Clarndon Press, Oxford, 1949.

G. G. Lorentz, Approximation of Functions. Scientific Research, Chelsea, New York, 1986.

B. K. Sendov and V. A. Popov, The averaged moduli of smoothness: applications in numerical methods and approximation (Pure and applied mathematics). Wiley, 1988.

N.B.Haasr and J. A. Sullivan, Real Analysis. Dover, 1991.

S. K. Jassim, "Direct and Inverse Inequalities for Some Discrete Operators by Bounded Measurable Functions," Serdica Bulgariacae Mathematicae Publications vol. 18, pp. 23-35, 1992.


Key Dates











Original Article

How to Cite

S. K. . Al-Saidy, H. W. Maktoof, A. K. O. . Mazeel, and B. G. Agaie, “On Best Multiplier Approximation of k-Monotone by Trigonometric Polynomial”, Al-Mustansiriyah Journal of Science, vol. 35, no. 1, pp. 88–94, Mar. 2024, doi: 10.23851/mjs.v35i1.1448.