پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 698 |
| تعداد مقالات | 10,090 |
| تعداد مشاهده مقاله | 71,240,636 |
| تعداد دریافت فایل اصل مقاله | 62,964,286 |
Uniqueness of meromorphic functions and nonlinear differential polynomials | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 09 آذر 1404 اصل مقاله (470.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33587.5015 | ||
| نویسندگان | ||
| Harina P Waghamore* ؛ B. E. Manjunath | ||
| Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India | ||
| تاریخ دریافت: 01 فروردین 1403، تاریخ بازنگری: 06 آذر 1403، تاریخ پذیرش: 13 آذر 1403 | ||
| چکیده | ||
| In this paper, we study the influence of the ``normal family" concept on the meromorphic functions $\xi_{1}(z)$ and $\xi_{2}(z)$ and the behavior of two nonlinear differential polynomials with a shared polynomial of a specific degree. Our investigation leads to uniqueness results for $\mathcal{P}(\xi_{1}(z))\mathcal{L}^{m}(\xi_{1}(z))$ and $\mathcal{P}(\xi_{2}(z))\mathcal{L}^{m}(\xi_{2}(z))$ under these circumstances. In addition, the results generalize and extend the findings of Cao and Zhang. | ||
| کلیدواژهها | ||
| Differential polynomial؛ Uniqueness؛ Meromorphic function؛ Normal family | ||
| مراجع | ||
|
[1] A. Banerjee, On a question of Gross, J. Math. Anal. Appl. 327 (2007), no. 2, 1232–1242. [2] S.S. Bhoosnurmath, B. Chakraborty, and H.M. Srivastava, A note on the value distribution of differential polynomials, Commun. Korean Math. Soc. 34 (2019), no. 4, 1145–1155. [3] Y.H. Cao and X.B. Zhang, Uniqueness of meromorphic functions sharing two values, J. Inequal. Appl. 2012 (2012), no. 1, 1–10. [4] J. Chang and L. Zalcman, Meromorphic functions that share a set with their derivatives, J. Math. Anal. Appl. 338 (2008), no. 2, 1020–1028. [5] H.H. Chen and M.L. Fang, The value distribution of f"f', Sci. China Ser. A 38 (1995), no. 7, 789–798. [6] M.L. Fang and X.H. Hua, Entire functions that share one value, Nanjing Daxue Xuebao Shuxue Bannian Kan 13 (1996), no. 1, 44–48. [7] W.K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. [8] L. Kohler and E. Mues, Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros, Complex Var. Elliptic Equ. 11 (1989), no. 1, 39–48. [9] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Elliptic Equ. 46 (2001), no. 3, 241–253. [10] I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), no. 1, 95–100. [11] M. Be and H.P. Waghamore, Uniqueness of meromorphic functions and their powers in set sharing, J. Appl. Anal. 30 (2024), no. 1, 157–172. [12] D.W. Meng, S.Y. Liu, and H.Y. Xu, Normal criteria of meromorphic functions concerning holomorphic functions, J. Comput. Anal. Appl. 27 (2019), no. 3, 511–524. [13] J. Schiff, Normal Families, Springer-Verlag, New York, 1993. [14] J.F. Xu, H.X. Yi, and Z.L. Zhang, Some inequalities of differential polynomials, Math. Inequal. Appl. 12 (2009), no. 1, 99–113. [15] C.C. Yang and X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), no. 2, 395–406. [16] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Math. Appl., vol. 557, Springer, Dordrecht, 2004. [17] Z.L. Zhang and W. Li, Picard exceptional-values for two differential polynomials, Chinese Sci. Abstracts Ser. A 5 (1995), no. 14, 1–10. [18] J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math. 8 (2007), no. 1, 1–10. | ||
|
آمار تعداد مشاهده مقاله: 87 تعداد دریافت فایل اصل مقاله: 79 |
||