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Turan-type inequalities for certain class of meromorphic functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 16، شماره 2، اردیبهشت 2025، صفحه 17-26 اصل مقاله (379.58 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29759.4249 | ||
| نویسندگان | ||
| Adil Hussain Malik* 1؛ Ajaz Ahmad Wani2 | ||
| 1Department of Mathematics, University of Kashmir, Srinagar-190006, India | ||
| 2Govt Degree College Pulwama, Pulwama-192301, India | ||
| تاریخ دریافت: 08 بهمن 1401، تاریخ پذیرش: 10 دی 1402 | ||
| چکیده | ||
| In this study, a broader class of rational functions r(u(z)) of degree mn, where u(z) is a polynomial of degree m is taken into consideration and obtain certain sharp compact generalization of well-known inequalities for rational functions. | ||
| کلیدواژهها | ||
| Rational function؛ Zeros؛ Poles | ||
| مراجع | ||
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[1] A. Aziz and B. Zargar, Some properties of rational functions with prescribed poles, Can. Math. Bull. 42 (1999), 417–426. [2] S. Bernstein, Sur l’ordre de la meilleure approximation des functions continues par des polynomes de degre donne, Mem. Acad. R. Belg. 4 (1912), 1–103. [3] V.N. Dubinin, On an application of conformal maps to inequalities for rational functions, Izv. Math. 66 (2002), 285–297. [4] V.K. Jain, Generalization of certain well-known inequalities for polynomials, Glas. Mate. 32 (1997), 45–51. [5] P.D. Lax, Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509–513. [6] X. Li, A comparison inequality for rational functions, Proc. Amer. Math. Soc., 139 (2011), 1659-1665. [7] X. Li, R.N. Mohapatra, and R.S. Rodriguez, Bernstein-type inequalities for rational functions with prescribed poles, J. London Math. Soc. 51 (1995), 523–531. [8] A.H. Malik, A note on sharpening of Erdos-Lax and Turan-type inequalities for a constrained polynomial, Int. J. Nonlinear Anal. Appl. 13 (2022), 3239–3249. [9] G.V. Milovanovic, A. Mir, and A. Hussain, Estimates for the polar derivative of a constrained polynomial on a disk, CUBO, A Math. J. 24 (2022), 541–554. [10] G.V. Milovanovic, A. Mir, and A. Hussain, Inequalities of Turan-type for algebraic polynomials, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116 (2022), no. 4, 154. [11] A. Mir and A. Hussain, Extremal problems of Turan-type involving the location of all zeros of a polynomial, Complex Variab. Elliptic Equ. (2023) 10.1080/17476933.2022.2158186. [12] P. Turan, Uber die ableitung von polynomen, Compos. Math. 7 (1939), 89–95. | ||
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