پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 687 |
| تعداد مقالات | 9,985 |
| تعداد مشاهده مقاله | 70,957,397 |
| تعداد دریافت فایل اصل مقاله | 62,422,644 |
Nevanlinna's counting functions for difference operators and related results | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 398، دوره 14، شماره 12، اسفند 2023، صفحه 359-371 اصل مقاله (390.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27770.3706 | ||
| نویسندگان | ||
| Audrija Choudhury* 1؛ Rupa Pal2 | ||
| 1Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Rd, Ballygunge, Kolkata-700019, West Bengal, India | ||
| 2Department of Mathematics, Bethune College, 181, Bidhan Sarani, Manicktala, Azad Hind Bag, Kolkata-700006, West Bengal, India | ||
| تاریخ دریافت: 20 تیر 1401، تاریخ بازنگری: 25 اسفند 1401، تاریخ پذیرش: 03 فروردین 1402 | ||
| چکیده | ||
| The study of the Nevanlinna theory for difference operators was introduced independently by Halburd & Korhonen and Chiang & Feng in the years 2006 and 2008 respectively. Halburd and Korhonen proved the uniqueness theorem for meromorphic functions associated with c-separated pairs. In this paper, we have generalised the result by introducing c-separated pairs of multiplicity p and their counting functions. We have deduced some analogues of certain unique results of classical Nevanlinna theory due to Chen, Chen & Tsai; Gopalakrishna & Bhoosnurmath; and Lahiri & Pal. Thereafter, we have also discussed certain implications of the deduced results. | ||
| کلیدواژهها | ||
| Meromorphic functions؛ c-separated pairs؛ Nevanlinna's counting functions؛ difference operator؛ periodic functions | ||
| مراجع | ||
|
[1] W. Bergweiler and J.K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Cambridge Phil. Soc. 142 (2007), no. 1, 133–147. [2] S.S. Bhoosnurmath, R.S. Dyavanal, M. Barki, and A. Rathod, Value distribution for n-th difference operator of meromorphic functions with maximal deficiency sum, J. Anal. 27 (2019), 797–811. [3] K.S. Charak, R.J. Korhonen, and G. Kumar, A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl. 435 (2016), no. 2, 1241–1248. [4] S. Chen, On uniqueness of meromorphic functions and their difference operators with partially shared values, Comput. Meth. Funct. Theory 18 (2018), 529–536. [5] T. Chen, K. Chen, and Y. Tsai, Some generalizations of Nevanlinna’s five-value theorem, Kodai Math. J. 30 (2007), no. 3, 438–444. [6] Z. Chen, Growth and zeros of meromorphic solution of some linear difference equations, J. Math. Anal. Appl. 373 (2011), no. 1, 235–241. [7] Z.X. Chen and K.H. Shon, On zeros and fixed points of differences of meromorphic functions, J. Math. Anal. Appl. 344 (2008), no. 1, 373–383. [8] P. Chern, On meromorphic functions with finite logarithmic order, Trans. Amer. Math. Soc. 358 (2006), no. 2, 473–489. [9] Y. Chiang and S. Feng, On the Nevanlinna characteristic of f(z + η) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105–129. [10] H.S. Gopalakrishna and S.S. Bhoosnurmath, Uniqueness theorems for meromorphic functions, Math. Scand. 39 (1976), no. 1, 125–130. [11] R. Halburd, R. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (2014), no. 8, 4267–4298. [12] R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477–487. [13] R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Scient. Fennic. Math. 31 (2006), 463–478. [14] W.K. Hayman, Meromorphic Functions, vol. 78, Oxford Clarendon Press, 1964. [15] J. Heittokangas, R. Korhonen, I. Laine, and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Variables Elliptic Equ. 56 (2011), no. 1-4, 81–92. [16] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352–363. [17] I. Lahiri and R. Pal, A note on Nevanlinna’s five value theorem, Bull. Korean Math. Soc. 52 (2015), no. 2, 345–350. [18] S. Li and Z. Gao, Entire functions sharing one or two finite values CM with their shifts or difference operators, Arch. Math. 97 (2011), no. 5, 475–483. [19] H. Liu and Z. Mao, On the meromorphic solutions of some linear difference equations, Adv. Differ. Equ. 2013 (2013), 1–12. [20] K. Liu, Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl. 359 (2009), no. 1, 384–393. [21] R. Nevanlinna, Zur theorie der meromorphen funktionen, Acta Math. 46 (1925), 1–99. [22] R. Nevanlinna, Einige eindeutigkeitssatze in der theorie der meromorphen funktionen, Acta Math. 48 (1926), no. 3-4, 367–391. [23] R. Nevanlinna, Le Theoreme de Picard-Borel et la Theorie des Fonctions Meromorphes, Gauthier Villars, Paris, 1929, reprint Chelsea Publ. Co., New York, 1974. [24] R. Pal and A. Choudhury, Some generalisations on the c-separated pairs and related results, Bull. Calcutta Math. Soc. 114 (2022), no. 2, 101–114. [25] X. Qi and L. Yang, Meromorphic functions that share values with their shifts or their n-th order differences, Anal. Math. 46 (2020), no. 4, 843–865. [26] X. Qi and L. Yang, Uniqueness of meromorphic functions with their n-th order differences, Bull. Iran. Math. Soc. 47 (2021), no. 5, 1491–1504. [27] C. C. Yang and H. X Yi, Uniqueness Theory of Meromorphic Functions, Science Press (Beijing/ New York) and Kluwer Academic Publishers (Dordrecht/ Boston/ London), 2003. [28] L. Yang, Value Distribution Theory, Springer-Verlag Berlin Heidelberg GmbH, 1993. | ||
|
آمار تعداد مشاهده مقاله: 44,307 تعداد دریافت فایل اصل مقاله: 50,337 |
||