The On Best Multiplier Approximation of K-Monotone Unbounded Functions by Spline Polynomials in L_(P,λ_n )-Space
Keywords:Multiplier Integral, Multiplier Averaged Modulus of Smoothness, Multiplier Norm, Spline Polynomial
The main purpose of this research is to study the degree of the best multiplier approximation of monotone unbounded functions in space, where by spline polynomials in terms of averaged multiplier modulus smoothness using some definitions and theorems necessary for this.
Y.-K. Hu, "Positive and copositive spline approximation in Lp [0, 1]," Computers & Mathematics with Applications, vol. 30, no. 3-6, pp. 137-146, 1995.
K. A. Kopotun, Approximation in Lp, 0< p< oo (Quasi) norm (Approximation Theory Viii-Volume 1: Approximation And Interpolation). World Scientific Publishing Co Pte Ltd, 1995.
Y. Hu, K. Kopotun, and X. Yu, "On Positive and Copositive Polynomial and Spline Approximation inLp [− 1, 1], 0< p<∞," journal of approximation theory, vol. 86, no. 3, pp. 320-334, 1996.
S. K. Al-Saidy and A. H. Zuboon, "Approximation of Unbounded Functions by Trigonometric Polynomials in Locally-Global Weighted " Al-Mustansiriya J. Sci., vol. 25, no. 3, pp. 97-112, 2014.
A. Pinkus, "Density in approximation theory," arXiv preprint math/0501328, 2005.
G. G. Lorentz, "Approximation of Functions," Scientific Research, Chelsea, New York, 1986.
B. Sendov and V. A. Popov, The averaged moduli of smoothness: applications in numerical methods and approximation. John Wiley & Sons Incorporated, 1988.
G. Hardy, "Divergent series," ed: Clavendan Press, 1949.
C. De Boor and C. De Boor, A practical guide to splines. springer-verlag New York, 1978.
G. I. Gaudry and I. R. Inglis, "Approximation of multipliers," Proceedings of the American Mathematical Society, vol. 44, no. 2, pp. 381-384, 1974.
M. J. Mohammed, and S. A. Abdul-Hammed. "On modified approximation properties by q-analogue summation-integral type operators." Journal of Kufa for Mathematics and Computer, vol. 3, no. 1, pp. 7-12, 2016.
Abdullah, G. "Negative Theorem for Lp, 0< P< 1 Monotone Approximation," Journal of Kufa for Mathematics and Computer vol. 4, no. 3, pp. 1-3, 2017.
How to Cite
Copyright (c) 2023 Hasan Maktoof, Saheb K. Al-Saidy, Abdul khaleq owaid mazeel
This work is licensed under a Creative Commons Attribution 4.0 International License.