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Integral inequality for the polar derivatives of polynomials | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 34، دوره 13، شماره 2، مهر 2022، صفحه 371-378 اصل مقاله (332.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25391.3001 | ||
| نویسنده | ||
| Xingjun Zhao* | ||
| School of Mathematics, Renmin University of China, Beijing, 100872, China | ||
| تاریخ دریافت: 08 آذر 1400، تاریخ بازنگری: 12 اردیبهشت 1401، تاریخ پذیرش: 14 اردیبهشت 1401 | ||
| چکیده | ||
| Let $P(z)$ be a polynomial of degree $n$ and for any complex number $\alpha$, let $$D_{\alpha}P(z)= nP(z) + (\alpha - z)P^{\prime}(z)$$ denote the polar derivative of $P(z)$ with respect to a complex number $\alpha$. In this paper, we prove some $L_{r}$ inequalities for the polar derivative of a polynomial have all zeros in $|z| \leq 1$. Our theorem generalizes a result of Dewan and Mir [K. K. Dewan, A. Mir, {\it Inequalities for the polar derivative of a polynomial}, J. Interd. Math. 10 (2007), no. 4, 525--531] and includes as special cases several interesting many known results. | ||
| کلیدواژه‌ها | ||
| Polar derivative؛ Inequality of polynomials؛ Integral inequality؛ Zeros | ||
| مراجع | ||
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