Uniqueness of meromorphic functions and their powers in set sharing

• Autorzy: Erajikkappa Manjunath , Waghamore Harina P.

Identyfikatory

DOI

10.1515/jaa-2023-0044

• Języki publikacji: EN

Abstrakty

EN

The objective of this study is to determine whether the existence of shared sets S containing both meromorphic (entire) functions and their higher derivatives, as well as powers of meromorphic functions and their differential polynomials, could result in uniqueness. The main focus is on determining the precise solutions to various differential equations. This problem is being studied in a broader context, specifically in set sharing.

Słowa kluczowe

EN

differential polynomials; uniqueness; meromorphic function; sharing sets

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2024
• Tom: Vol. 30, nr 1
• Strony: 157--172
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Erajikkappa Manjunath

• Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore 560 056, India

• https://orcid.org/0000-0002-9467-705X

autor

Waghamore Harina P.

• Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore 560 056, India

• https://orcid.org/0000-0002-5381-2315

Bibliografia

• [1] A. Banerjee and M. B. Ahamed, Meromorphic function sharing a small function with its differential polynomial, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 54 (2015), no. 1, 33-45.
• [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] J. Chang, M. Fang and L. Zalcman, Entire functions that share a set with their derivatives, Arch. Math. (Basel) 89 (2007), no. 6, 561-569.
• [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] M. Fang and L. Zalcman, Normal families and uniqueness theorems for entire functions, J. Math. Anal. Appl. 280 (2003), no. 2, 273-283.
• [6] W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964.
• [7] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.
• [8] F. Lü, A note on meromorphic functions that share a set with their derivatives, Arch. Math. (Basel) 96 (2011), no. 4, 369-377.
• [9] A. Z. Mokhon’ko, The Nevanlinna characteristics of certain meromorphic functions, Funct. Anal. Appl. 14 (1971), 83-87.
• [10] E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206.
• [11] L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, in: Complex Analysis, Lecture Notes in Math. 599, Springer, Berlin (1977), 101-103.
• [12] H. X. Yi, Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Variables Theory Appl. 14 (1990), no. 1-4, 169-176.
• [13] H.-X. Yi, Uniqueness theorems for meromorphic functions. II, Indian J. Pure Appl. Math. 28 (1997), no. 4, 509-519.
• [14] H.-X. Yi, Uniqueness theorems for meromorphic functions whose nth derivatives share the same 1-points, Complex Variables Theory Appl. 34 (1997), no. 4, 421-436.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).