پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,027 |
| تعداد مشاهده مقاله | 67,082,815 |
| تعداد دریافت فایل اصل مقاله | 7,656,333 |
Growth of the sth derivative of a polynomial with restricted zeros | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 7، مهر 2024، صفحه 1-9 اصل مقاله (383.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27169.3521 | ||
| نویسندگان | ||
| Reingachan Ngamchui؛ Khangembam Babina Devi* ؛ Barchand Chanam | ||
| Department of Mathematics, National Institute of Technology Manipur, Manipur-795004, India | ||
| تاریخ دریافت: 24 اردیبهشت 1401، تاریخ بازنگری: 19 مرداد 1402، تاریخ پذیرش: 21 مرداد 1402 | ||
| چکیده | ||
| In this paper, we establish some upper bound estimates for the maximum modulus of the higher order derivative of a polynomial with restricted zeros on a circle of $|z|=R$, $R\geq 1$, in terms of the maximum modulus of the same polynomial on the unit circle $|z|=1$. These results generalize and sharpen some known results in this direction. | ||
| کلیدواژه‌ها | ||
| Polynomials؛ Zeros؛ Inequalities؛ Maximum modulus | ||
| مراجع | ||
|
[1] N.C. Ankeny and T.J. Rivlin, On a theorem of S. Bernstein, Pacific J. Math., 5 (1955), 849-862. [2] A. Aziz and N.A. Rather, Some Zygmund type Lq inequalities for polynomials, J. Math. Anal. Appl. 289 (2004), 14–29. [3] A. Dalal and N.K. Govil, On sharpening of a theorem of Ankeny and Rivlin, Anal. Theory. Appl. 36 (2018), 225–234. [4] K.B. Devi, T.B. Singh, R. Singh and B. Chanam, Growth of polynomials not vanishing inside a circle, J. Anal. 30 (2022), 1439–1454. [5] K.K. Dewan and A.A. Bhat, On the maximum modulus of a polynomials not vanishing inside a unit circle, J. Interdiscip. Math. 1 (1998), 129–140. [6] R.B. Gardner, N.K. Govil and S.R. Musukula, Rate of growth of polynomials not vanishing inside a circle, J. Inequal. Pure Appl. Math. 6 (2005), Art. 53. [7] N.K. Govil, On the maximum modulus of polynomials not vanishing inside the unit circle, Approx. Theory Appl. 5 (1989), 79–82. [8] N.K. Govil, Some inequalities for derivatives of polynomials, J. Approx. Theory 66 (1991), 29–35. [9] N.K. Govil and G. Nyuydinkong, On the maximum modulus of polynomials not vanishing inside a circle, J. Interdiscip. Math. 4 (2001), 93–100. [10] I. Hussain, Growth estimates of a polynomial not vanishing in a disk, Indian J. Pure Appl. Math. 53 (2021), 750–759. [11] A. Mir, A. Ahmad and A.H. Malik, Growth of a polynomial with restricted zeros, J. Anal. 28 (2020), 827–837. [12] G. Polya and G. Szego, Aufgaben and Leheatze ous der Analysis, Springer-Verlag, Berlin, 1925. | ||
|
آمار تعداد مشاهده مقاله: 13,132 تعداد دریافت فایل اصل مقاله: 204 |
||