Weighted Moduli of Smoothness and Sign-Preserving Approximation

• Date: 2005
• Main Authors: Smazhenko, I. V., Смаженко, І. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3608
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider a continuous function that changes its sign on an interval finitely many times and pose the problem of the approximation of this function by a polynomial that inherits its sign. For this approximation, we obtain (in the case where this is possible) Jackson-type estimates containing modif...