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Turan type inequalities for rational functions with prescribed poles | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 83، دوره 13، شماره 1، خرداد 2022، صفحه 1003-1009 اصل مقاله (309.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23145.2484 | ||
| نویسندگان | ||
| Tawheeda Akhter* 1؛ Shabir Ahmad Malik2؛ Bashir Ahmad Zargar3 | ||
| 1Naseem Bagh Srinagar | ||
| 2Department of Mathematics, University of Kashmir , Srinagar, Jammu and Kashmir, India | ||
| 3University of Kashmir | ||
| تاریخ دریافت: 26 فروردین 1400، تاریخ بازنگری: 24 مرداد 1400، تاریخ پذیرش: 30 مرداد 1400 | ||
| چکیده | ||
| In this paper, we establish some inequalities for rational functions with prescribed poles having t-fold zeros at the origin. The estimates obtained generalise as well as refine some known results for rational functions and in turn, produce extensions of some polynomial inequalities earlier proved by Turan, Jain etc. | ||
| کلیدواژهها | ||
| Rational functions؛ inequalities in complex domain؛ poles؛ t-fold zeros | ||
| مراجع | ||
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[1] A. Aziz and Q.M. Dawood, Inequalities for a polynomial and its derivative, J. Approx. Theory 54 (1998) 306–313. [2] A. Aziz and W.M. Shah, Some refinements of Bernstein type inequalities for rational functions, Glas. Mat. Ser. iii 32 (1997) 29–37. [3] A. Aziz and W.M. Shah, Some properties of rational functions with prescribed poles and restricted zeros, Math. Balkanica (N.S) 18 (2004) 33–40. [4] A. Aziz and B.A. Zargar, Some properties of rational functions with prescribed poles, Canad. Math. Bull. 42 (1999) 417–426. [5] S. N. Bernstein, Sur l’ordre de la meilleure approximation des functions continues par des polynˆomes de degr´e donn´e, Mem. Acad. R. Belg. 4 (1912) 1–103. [6] V. K. Jain, Inequalities for a polynomial and its derivative, Proc. Indian Acad. Sci. (Math. Sci.) 110 (2000) 137–146. [7] Xin Li, A comparison inequality for rational functions, Proc. Amer. Math. Soc. 139 (2011) 1659–1665. [8] Xin Li, R. N. Mohapatra and R. S. Rodriguez, Bernstein type inequalities for rational functions with prescribed poles, J. Lond. Math. Soc. 51 (1995) 523–531. [9] G.V. Milovanovi´c and A. Mir, Comparison inequalities between rational functions with prescribed poles, Rev. R. Acad. Cienc. Exactas. Fis. Nat. Ser. A. Mat. 115 (2021) 1–13. [10] P. Turan, Uber die Ableitung von polynomen ¨ , Compositio Math. 7 (1939) 89–95. | ||
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