Geodesic
A normal criterion concerning sequence of functions and their differential polynomials
Problemy analiza, Tome 13 (2024) no. 2, pp. 3-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study normality of a sequence of meromorphic functions whose differential polynomials satisfy a certain condition. We also give examples to show that the result is sharp.
Keywords: normal families, differential polynomials, meromorphic functions. 
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N. Bharti. A normal criterion concerning sequence of functions and their differential polynomials. Problemy analiza, Tome 13 (2024) no. 2, pp. 3-24. http://geodesic.mathdoc.fr/item/PA_2024_13_2_a0/

[1] Aladro G., Krantz S. G., “A criterion for normality in $\mathbb{C}^{n}$”, J. Math. Anal. Appl., 161 (1991), 1–8 | DOI | MR | Zbl

[2] Beardon A. F., Minda D., “Normal families: a geometric perspective”, Comput. Methods Funct. Theory, 14 (2014), 331–355 | DOI | MR | Zbl

[3] Chang J. M., “Normality and quasinormality of zero-free meromorphic functions”, Acta Math. Sin. Engl. Ser., 28:4 (2012), 707–716 | DOI | MR | Zbl

[4] Chang J. M., Xu Y., Yang L., “Normal families of meromorphic functions in several variables”, Comput. Methods Funct. Theory, 2023 | DOI | MR

[5] Charak K. S., Rochon D., Sharma N., “Normal families of bicomplex holomorphic functions”, Fractals, 17:2 (2009), 257–268 | DOI | MR | Zbl

[6] Charak K. S., Rochon D., Sharma N., “Normal families of bicomplex meromorphic functions”, Ann. Polon. Math., 103 (2012), 303–317 | DOI | MR | Zbl

[7] Charak K. S., Sharma N., “Bicomplex analogue of Zalcman lemma”, Complex Anal. Oper. Theory, 8:2 (2014), 449–459 | DOI | MR | Zbl

[8] Chen Q. Y., Yang L., Pang X. C., “Normal family and the sequence of omitted functions”, Sci. China Math., 9 (2013), 1821–1830 | DOI | MR | Zbl

[9] Chen H. H., Gu Y. X., “Improvement of Marty's criterion and its application”, Science in China Ser. A, 36:6 (1993), 674–681 | MR | Zbl

[10] Chen S., Xu Y., “Normality relationships between two families concerning shared values”, Monatsh. Math., 196 (2021), 1–13 | DOI | MR | Zbl

[11] Deng B. M., Fang M. L., Liu D., “Normal families of zero-free meromorphic functions”, J. Aust. Math. Soc., 91 (2011), 313–322 | DOI | MR | Zbl

[12] Deng H., Ponnusamy S., Qiao J., “Properties of normal harmonic mappings”, Monatsh. Math., 193:3 (2020), 605–621 | DOI | MR | Zbl

[13] Deng B. M., Yang D. G., Fang M. L., “Normality concerning the sequence of functions”, Acta Math. Sin. Eng. Ser., 33:8 (2017), 1154–1162 | DOI | MR | Zbl

[14] Dethloff G., Tan T. V., Thin N. V., “Normal criteria for families of meromorphic functions”, J. Math. Anal. Appl., 411:2 (2014), 675–683 | DOI | MR | Zbl

[15] Fujimoto H., “On families of meromorphic maps into the complex projective space”, Nagoya Math. J., 54 (1974), 21–51 | DOI | MR | Zbl

[16] Grahl J., “Hayman's alternative and normal families of non-vanishing meromorphic functions”, Comput. Methods Funct. Theory, 2 (2004), 481–508 | DOI | MR

[17] Gu Y. X., “A normal criterion of meromorphic families”, Sci. Sin., 1 (1979), 267–274 | Zbl

[18] Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964 | MR | Zbl

[19] Hayman W. K., Research Problems in Function Theory, Athlone Press, London, 1967 | MR | Zbl

[20] Kim K. T., Krantz S. G., “Normal families of holomorphic functions and mappings on a Banach space”, Expo. Math., 21 (2003), 193–218 | DOI | MR | Zbl

[21] Kumar R., Bharti N., “Normal families concerning partially shared and proximate values”, Sgo Paulo J. Math. Sci., 17 (2023), 1076–1085 | DOI | MR

[22] Montel P., “Sur les suites infinies desfonctions”, Ann. $\acute{E}$cole. Norm. Sup., 24 (1907), 233–334 | DOI | MR

[23] Montel P., “Sur les families de fonctions analytiques qui admettent des valeurs exceptionnelles dans un domaine”, Ann. $\acute{E}$cole. Norm. Sup., 29:3 (1912), 487–535 | DOI | MR

[24] Pang X. C., Zalcman L., “Normal families and shared values”, Bull. Lond. Math. Soc., 32:3 (2000), 325–331 | DOI | MR | Zbl

[25] Schiff J. L., Normal Families, Springer, Berlin, 1993 | MR | Zbl

[26] Thin N. V., “Normal family of meromorphic functions sharing holomorphic functions and the converse of the Bloch principle”, Acta Math. Sci., 37B:3 (2017), 623–656 | DOI | MR | Zbl

[27] Thin N. V., “Normal criteria for family meromorphic functions sharing holomorphic function”, Bull. Malays. Math. Sci. Soc., 40 (2017), 1413–1442 | DOI | MR | Zbl

[28] Thin N. V., Oanh B. T. K., “Normality criteria for families of zero-free meromorphic functions”, Analysis, 36:3 (2016), 211–222 | DOI | MR | Zbl

[29] Yang L., “Normality for families of meromorphic functions”, Sci. Sin., 29 (1986), 1263–1274 | MR | Zbl

[30] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993 | MR | Zbl

[31] Wu H., “Normal families of holomorphic mappings”, Acta Math., 119 (1967), 193–233 | DOI | MR | Zbl

[32] Xie J., Deng B. M., “Normality criteria of zero-free meromorphic functions”, Chin. Quart. J. Math., 34:3 (2019), 221–231 | MR | Zbl

[33] Zalcman L., “A heuristic principle in complex function theory”, Amer. Math. Monthly, 82 (1975), 813–817 | DOI | MR | Zbl

[34] Zalcman L., “Normal families: new perspectives”, Bull. Amer. Math. Soc., 35 (1998), 215–230 | DOI | MR | Zbl