The shared set and uniqueness of algebroid functions on annuli

Downloads

Abstract

In this paper, we discuss the shared set and uniqueness of algebroid function on annuli.

Keywords:

Value Distribution Theory, algebroid functions, annuli.

Mathematics Subject Classification:

Mathematics
  • Ashok Rathod Department of Mathematics, K.L.E Society’s G. I. Bagewadi Arts Science and Commerce College, Nipani, Karnataka- 591237, India.
  • Praveen Basavanneppa Burji Department of Mathematics, S. S. Arts College and T. P. Science Institute, Sankeshwar, Karnataka-591313, India.
  • Pages: 1047-1056
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

Ullarich E. Uber den Einfluess der verzweigtheit einer algebloide auf ihre wertvertellung, J Reine Angew math, $169(1931), 198-220$.

Valiron, G. Sur quelques proprietes des fonctions algebroldes. Comptes Rendus Mathematique. Academie des Sciences. Paris, 189(1929), 824-826.

Baganas, N. Sur les valeurs algebriques dune fonctions algebroldes et les integrales psendo-abelinnes, Annales Ecole Norm. Sup., 66(1949), 161-208.

Gopalkrishna H. S, Bhooanurmath S. S. Exceptional values of meromorphic functions, Annales Polonici Mathe matici, 32(1976), 83-93.

Singh S. K, Gopalkrishna H. S. Exceptional values of entire and meromorphic functions, Mathematische Annalen, 191(1976), 121-142.

Yu-Zan He and Ye-Zhou Li. Some results on algebroid functions, Complex variables, 43(2001), 299-313.

Daochun S, Zongsheng G. On the operation of algebroid functions, Acta Mathematica Scientia; (2010), 247-256.

Daochun S, Zongsheng G. Value disribution theory of algebroid functions, Beijing: Science Press, 2014.

Yu-Zan He and Xiu-Zhi Xiao. Algebroid functions and Ordinarry Difference Equations, Beijing; Science Press, 1988.

Daochun S, Zongsheng G. Theorems for algebroid functions, Acta Math. Sinica, 49(2006), 1-6.

Hongxun Y. On the multiple values and uniqueness of algebroid functions, Eng.Math., 8(1991), 1-8.

Hayman W K. Meromorphic functions, Oxford: Oxford University Press, 1964.

Minglang $mathrm{F}$. Unicity theorem for algebroid functions, Acta. Math. Sinica, 36(1993), 217-222.

Pingyuan Zhang, Peichu $mathrm{Hu}$. On uniqueness for algebroid functions of finite order, Acta. Math. Sinica, 35(2015), $630-638$

Prokoporich G S. Fix-points of meromorphic or entire functions, Ukrainian Math J, 25(1937), 248-260.

Qingcai Z. Uniqueness of algebroid functions, Math. Pract. Theory, 43(2003), 183-187.

Cao Tingbin, Yi Hongxun. On the uniqueness theory of algebroid functions, Southest Asian Bull.Math. 33(2009), $25-39$

Yang $mathrm{C} . mathrm{C}, mathrm{Yi} mathrm{H} . mathrm{X}$. Uniqueness theory of meromorphic functions, Science Press, 1995, Kluwer.

Yi H. X. The multiple values of meromorphic functions and uniqueness, Chinese Ann. Math. Ser. A, 10(1989), 421-427.

R. S. Dyavanal, Ashok Rathod. Uniqueness theorems for meromorphic functions on annuli, Indian Journal of Mathematics and Mathematical Sciences, 12(2016), 1-10.

R. S. Dyavanal, Ashok Rathod, Multiple values and uniqueness of meromorphic functions on annuli, International Journal Pure and Applied Mathematics, 107(2016), 983-995.

R. S. Dyavanal, Ashok Rathod. On the value distribution of meromorphic functions on annuli, Indian Journal of Mathematics and Mathematical Sciences, 12(2016), 203 217.

Ashok Rathod. The multiple values of algebroid functions and uniqueness, Asian Journal of Mathematics and Computer Research, 14(2016), 150-157.

Ashok Rathod. The uniqueness of meromorphic functions concerning five or more values and small functions on annuli, Asian Journal of Current Research, 1(2016), 101 107.

Ashok Rathod. Uniqueness of algebroid functions dealing with multiple values on annuli, Journal of Basic and Applied Research International, 19(2016), 157-167.

Ashok Rathod. On the deficiencies of algebroid functions and their differential polynomials, Journal of Basic and Applied Research International, 1(2016), 1-11.

R. S. Dyavanal, Ashok Rathod. Some generalisation of Nevanlinna's five-value theorem for algebroid functions on annuli, Asian Journal of Mathematics and Computer Research, 20(2017), 85-95.

R. S. Dyavanal, Ashok Rathod. Nevanlinna's five-value theorem for derivatives of meromorphic functions sharing values on annuli, Asian Journal of Mathematics and Computer Research, 20(2017), 13-21.

R. S. Dyavanal, Ashok Rathod. Unicity theorem for alge-broid functions related to multiple values and derivatives on annuli, International Journal of Fuzzy Mathematical Archive, 13(2017), 25-39.

R. S. Dyavanal, Ashok Rathod. General Milloux inequality for algebroid functions on annuli, International Journal of Mathematics and applications, 5(2017), 319-326.

Ashok Rathod. The multiple values of algebroid functions and uniqueness on annuli, Konuralp Journal of Mathematics, 5(2017), 216-227.

Ashok Rathod. Several uniqueness theorems for algebroid functions, J. Anal., 25(2017), 203-213.

Ashok Rathod. Nevanlinna's five-value theorem for algebroid functions, Ufa Mathematical Journal; 10(2018), $127-132$.

Ashok Rathod. Nevanlinna's five-value theorem for derivatives of algebroid functions on annuli, Tamkang Journal of Mathematics; 49(2018), 129-142.

S. S. Bhoosnurmath, R. S. Dyavanal, Mahesh Barki, Ashok Rathod. Value distribution for $n$ 'th difference operator of meromorphic functions with maximal deficiency sum, J Anal, 27(2019), 797-811.

Ashok Rathod. Characteristic function and deficiency of algebroid functions on annuli, Ufa Mathematical Journal; $11(2019), 121-132$.

Ashok Rathod. Value distribution of a algebroid function and its linear combination of derivatives on annuli, Electronic Journal of Mathematical analysis and applications; $8(2020), 129-142$.

Ashok Rathod. Uniqueness theorems for meromorphic functions on annuli, Ufa Mathematical Journal; 12(2020), $115-121$

A. Ya. Khrystiyanyn, A. A. Kondratyuk. On the Nevanlinna Theory for meromorphic functions on annuli. I, Mathematychin Studii, 23(2005), 19-30.

A. Ya. Khrystiyanyn, A. A. Kondratyuk. On the Nevanlinna Theory for meromorphic functions on annuli. II, Mathematychin Studii, 24(2005), 57-68.

T.B.Cao, H. X. Yi, H. Y. Xu. On the multiple values and uniqueness of meromorphic functions on annuli, Com. pute. Math. Appl., 58(2009), 1457-1465.

A. Fernandez. On the value distribution of meromorphic function in the punctured plane, Mathematychin Studii, 34(2010), 136-144.

Yang Tan, Yue Wang. On the multiple values and uniqueness of algebroid functions on annuli, Complex variable and elliptic equations, 60(2015), 1254-1269.

Yang Tan. Several uniqueness theorems of algebroid functions on annuli, Acta Mathematica Scientia, 36(2016), $295-316$

T.B. Cao, Z. S. Deng. On the uniqueness meromorphic functions that share three or two sets on annuli, Proceedings of the Indian Academy of Sciences, 122(2012), $355-369$.

G. Frank, M. Reinders. A unique range set for meromorphic functions with 11 elements, Complex Variables, $$

(1998), 185-193 .

$$

A. Z. Mokhon'ko. The Nevanlinna characteristics of some meromorphic functions, Functional Analysis and Their Applications, 14(1971), 83-87.

Metrics

Metrics Loading ...

Published

01-01-2021

How to Cite

Ashok Rathod, and Praveen Basavanneppa Burji. “The Shared Set and Uniqueness of Algebroid Functions on Annuli”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 1047-56, https://www.malayajournal.org/index.php/mjm/article/view/1217.

Issue

Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

Section

Articles

License

Copyright (c) 2021 MJM

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.