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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications
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Volume 11Issue 1PP: 47-53 • 2024

On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces

Sergey Drominko 1* ,
Erina Kovachiskaya 1
1Faculty of Information Technology and Robotics, Vitebsk State Technological University, Belarus
* Corresponding Author.
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: October 27, 2023 Revised: March 02, 2024 Accepted: June 29, 2024

Abstract

In this paper, we study of the Markov- Bernstein inequality of a complex polynomial with exponential weight functions  e^(-r^2  z/2)   on the domain ├]-∞,+∞┤[,    we also study the Integral Markov-Bernstein inequality for the algebraic polynomials of degree 2m and degree m with algebraic weight functions on the domain [1,+∞┤[of type (1/x^2 )^(-n), and on the domain ├]0,+∞┤[of type (1/t)^(-n).

Keywords

Markov &ndash Bernstein inequality weight functions Weight Space Lp-space

References

[1]       L. Lukashov, Inequalities for the derivatives of rational functions on several intervals. Izv. Ross. Akad. Nauk Ser. Mat., 68(2004), 115–138,(Russian); English translation in Izv. Math., 68(2004), 543 565.

[2]       Serge kalmykov Be`la Nagy and Vilmos Totik, Bernestein- and Markov-Type inequalities, arxiv: 2014.0234V2 (math.ev) 21 May2021.

[3]       GUVEN.A; ISRAFILOV, D-M. Multiplier Theorems in Weighted smirnov space. J.Korean Math Soc, 45, No 6, 2008, 1535-1548.

[4]     T.Kilgore, Inter polation properties of polynomial of degree at most 2n Weighted by

[5]       T.Kilgore, Markov and Bernstien inequalities in Lp for some Weighted algebraic and trigonometric poly mails, Journal of Inequalities and Application.4 (2005), 413-321.

[6]       V. Totik, Bernstein and Markov type inequalities for trigonometric polynomials on general sets. Int. Math. Res. Not., IMRN, 11(2015), 2986–3020.

[7]       Nagy and F. To´okos, Bernstein inequality in Lα norms. Acta Sci.Math. (Szeged), 79(2013), 129–174.

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Drominko, Sergey, Kovachiskaya, Erina. "On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 1, 2024, pp. 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105
Drominko, S., Kovachiskaya, E. (2024). On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 1), 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105
Drominko, Sergey, Kovachiskaya, Erina. "On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces." Galoitica: Journal of Mathematical Structures and Applications Volume 11, no. Issue 1 (2024): 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105
Drominko, S., Kovachiskaya, E. (2024) 'On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces', Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 1), pp. 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105
Drominko S, Kovachiskaya E. On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications. 2024;Volume 11(Issue 1):47-53. DOI: https://doi.org/10.54216/GJMSA.0110105
S. Drominko, E. Kovachiskaya, "On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 1, pp. 47-53, 2024. DOI: https://doi.org/10.54216/GJMSA.0110105
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