Negative theorem for r-monotone approximation

Ajel, Wahlaa Abass; Bhaya, Eman S.

doi:10.47974/JIM-1746

Open Access Research Article

Negative theorem for r-monotone approximation

^*Wahlaa Abass AjelCorresponding authorwahlaaabass@gmail.comDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, IraqView full profile → , Eman S. Bhayaemanbhaya@uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, IraqView full profile →

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pp. 691–697Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1746XML

Received:: 13 Sep 2023
Published Online:: 31 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1746
Pages:: 691–697

Abstract

Recently, many theorems were introduced for monotone, convex, 3-monotone approximation, r-monotone for functions in Lp Quasi-normed space. Now, there is a question: can we strengthen these results in terms of moduli of smoothness of higher order? The answer is no, which we see in our work here. Here, we introduce the negative theorem for the r-monotone approximation of function in Lp Quasi-normed space for 0 < p < 1.

Keywords

Negative theorem Quasi normed space R-monotone approximation

Subject Classifications

34C1247H05

References

[1] E. S. Bhaya, B. K. Hussein, A new modulus of smoothness for uniform approximation, J. Univ. Babylon, Pure & Appl. Sci, 26, 8-15 (2018).
[2] E. S. Bhaya, H. A. Almurieb, The degree of best neural networks approximation with application, (Unpublished doctoral dissertation) Babylon University, Babylon, Iraq (2020).
[3] G. G. LORENTZ AND K. ZELLER, Degree of approximation by monotone polynomials. II. J. Approx. Theory 2, 265-269 (1969).
[4] K. A. Kopotun, K. D.Leviatan, &I.A.Shevchuk, Interpolatorypointwise estimates for monotone polynomial approximation. J. Math.Anal. Appl, 459, 1260-1295 (2018).
[5] K. A. Kopotun, K. D. Leviatan, & I. A. Shevchuk, Uniform and pointwise shape preserving approximation (SPA) by algebraic polynomials: an update, SMAI Journal of Computational Mathematics, S5, 99-108 (2019).
[6] K. G. Steffens, The history of approximation theory, Birkhauser Boston, P. 219 (2006), 0-8176-4353-2.
[7] S. K. AL-Saidy, H.W. Maktoof, & A. O. Mazed, On best multiplier approximation of k-monotone of. Journal of Education for Pure Science- University of Thi-Qar, 12, 275-283 (2022).
[8] X. WU, On a Counterexample in monotone approximation, Journal of Approximation Theory, 69, 205-211 (1992).
[9] Shelash, Hader Baqer, Ahmad, Hasanain Hamid & Obaid, Ahmed J. On characterizations some of subgroups of the dihedral group D2n, Journal of Discrete Mathematical Sciences and Cryptography, 1-6, DOI: 10.47974/JDMSC-1553.
[10] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611.

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