Piecewise Monotone Approximation of Unbounded Functions In Weighted Space LP,w([-,])

Adnan, Alaa; Mehiady, Sultan

doi:10.37652/juaps.2022.174841

Document Type : Research Paper

Authors

Alaa Adnan ¹
Sultan Mehiady ²

¹ Department of Mathematics,College of Education for pure science, University of Anbar, Ramadi,Iraq

² Department of Mathematics,College of Education for pure science,University of Anbar, Ramadi,Iraq

https://doi.org/10.37652/juaps.2022.174841

Abstract

In this paper, investigate the approximation of unbounded functions in weighted space, by using trigonometric polynomials considered. We introduced type of polynomials piecewise monotone having same local monotonicity as unbounded functions without affecting the order of huge error have a finite number of max. and min. unbounded functions that amount. In addition, we established not included any of extreme points of this functions, of and closed subset γ on closed intervals then there exist class of polynomials such that the best of approximation has high or order of and such that for sufficiently great of the polynomials and functions have the same monotonicity at each of γ.

Keywords

Main Subjects

Mathematical

References

[1] Darst R. B. and sahib s., (1983),Approximation of continuous and quasi – continuous functions by monotone Functions, j. Approx. Theory 38 ,p.p. 9 – 27.

[2] Hectare R. , (1985), Best L1 –approximation of quasi – continuous functions on[0,1] by non-decreasing functions, Functions, j. Approx. Theory 44, p.p. 221 – 229. J. New York. Devore A. and Lorentz G., (1993), Constructive Approximation, Springer-verlag [3]

[4] Leviathan D. , (1998) ,Monotone approximation estimates involving the third modulus of smoothness, Approximation I.( Nashville, TN, 1998), Innov – App..Math. Vanderbilt univ. press, Nashville, TN, ,p Theory IX, Nol..p.233 – 230.

[5] Koptune K.A., (1994), ,Point wise and uniform estimates for convex approximation of functions by Algebraic polynomial , Constar. Approx. to ,p.p.153-178.

[6] Wilbert D., (2004) , Best approximation by the inverse of a monotone polynomial and location problem, J. Approx. Theory (114), 98 – 114.

[7] Alaa A.A. and Alaa M., (2017), co positive approximation of unbounded functions in weighted space,international Of Applied Engineering Research, vol.12 No. 21 , p.p. 11392 – 11396. Journal

[8] Koptune K.A., Leviahan D. and shevechuk, I. A., (2011), uniform and point wise shape preserving approximation by Algebraic polynomials, surv. Approx. Theory 6 24 – 74.

[9] Dzyubenko, G.A., Leviathan D., (2014), point wise estimates of convex approximation, Jaen J. Approx 6 ,P.P. 261 – 295.

[10] Leviathan D. and petrova I. L. ,(2017), interpolatory estimates in monotone piecewise polynomial approximation J. Approx. Theory 233 ,p.p. 1 – 8.

Journal of University of Anbar for Pure Science

Piecewise Monotone Approximation of Unbounded Functions In Weighted Space LP,w([-,])

References

References

Volume 16, Issue 1 - Issue Serial Number 1
July 2022
Page 65-68

Piecewise Monotone Approximation of Unbounded Functions In Weighted Space LP,w([-,])

References

References

Volume 16, Issue 1 - Issue Serial Number 1July 2022Page 65-68

Volume 16, Issue 1 - Issue Serial Number 1
July 2022
Page 65-68