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Inequalities for a class of rational functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 54، دوره 13، شماره 2، مهر 2022، صفحه 609-617 اصل مقاله (344.64 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.25521.3042 | ||
| نویسندگان | ||
| Mohd Yousf Mir* ؛ Lubna Wali Shah؛ Wali Mohammad Shah | ||
| Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India | ||
| تاریخ دریافت: 17 مهر 1400، تاریخ بازنگری: 20 آذر 1400، تاریخ پذیرش: 24 آذر 1400 | ||
| چکیده | ||
| In this paper, we consider a more general class of rational functions $r(s(z)),$ of degree $mn,$ with $s(z)$ being a polynomial of degree $m.$ Our results not only generalize the results due to Wali and Shah [JOA, \textbf{25} (2017), no. 1, 43-53] but also improve the results obtained by Qasim and Liman [Indian. J. Pure Appl. Math. \textbf{46} (2015), no. 3, 337-348] and Mir [Indian J. Pure Appl. Math. \textbf{50} (2019), no. 2, 315-331]. | ||
| کلیدواژه‌ها | ||
| Rational Function؛ Polynomials؛ Zeros؛ Poles؛ Inequalities | ||
| مراجع | ||
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[1] A. Mir, Inequalities concerning rational functions with prescribed poles, J. Pure Appl. Math. 50 (2019), no. 2, 315–331. [2] A. Mir, Some inequalities concerning rational functions with fixed poles, J. Contemp. Math. Anal. 55 (2020), no. 2, 105–114. [3] A. Aziz and Q.M. Dawood, Inequalities for polynomials and its derivative, Indian J.Approx. Theory 54 (1988), 119–122. [4] S.N. Bernstein, Sur la limitation des derives des polynomes, C. R. Acad. Sci. Paris. 190 (1930), 338–340. [5] I. Qasim and A. Liman, Bernstein type inequalities for rational functions, Indian. J. Pure Appl. Math. 46 (2015), no. 3, 337–348. [6] R. Osserman, A sharp Schwarz inequality on the boundary for functions regular in disk, Proc. Amer. Math. Soc. 128 (2000), no. 12, 3513–3517. [7] P. Tur´an, Uber die ableitung von polynomen, ¨ Compos. Math. 7 (1939), 89–95. [8] S.L. Wali and W.M. Shah, Some applications of Dubinin’s lemma to rational functions with prescribed poles, J. Math. Anal. Appl. 450 (2017), 769–779. [9] S.L. Wali and W.M. Shah, Applications of the Schwarz lemma to inequalities for rational functions with prescribed poles, J. Anal. 25 (2017), no. 1, 43–53. [10] X. Li, R.N. Mohapatra and R.S. Rodriguez, Bernstein-type inequalities for rational functions with prescribed poles, J. London Math. Soc. 51 (1995), 523–53 | ||
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