On Hilbert's 17th Problem and Real Nullstellensatz for Global Analytic Functions.
Jesus M. Ruiz (1985)
Mathematische Zeitschrift
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Jesus M. Ruiz (1985)
Mathematische Zeitschrift
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Jesús M. Ruiz (1984)
Manuscripta mathematica
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Evgeny M. Chirka (1996)
Publicacions Matemàtiques
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If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.
Xiao-Min Li, Hong-Xun Yi (2010)
Annales Polonici Mathematici
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We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.
Jun-Fan Chen (2017)
Open Mathematics
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We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
Wei-Ran Lü, Hong-Xun Yi (2003)
Annales Polonici Mathematici
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We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.
Xiao-Min Li, Hong-Xun Yi (2009)
Annales Polonici Mathematici
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We deal with a uniqueness theorem of two meromorphic functions that share three values with weights and also share a set consisting of two small meromorphic functions. Our results improve those by G. Brosch, I. Lahiri & P. Sahoo, T. C. Alzahary & H. X. Yi, P. Li & C. C. Yang, and others.
Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)
Open Mathematics
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In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
Indrajit Lahiri, Arindam Sarkar (2005)
Annales Polonici Mathematici
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We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.
S. K. Bajpai, T. J. S. Mehrok (1975)
Annales Polonici Mathematici
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Xiu-Qing Lin, Wei-Chuan Lin (2011)
Annales Polonici Mathematici
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This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].
Abhijit Banerjee, Molla Basir Ahamed (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove the uniqueness of meromorphic functions sharing some three sets with finite weights.
Hong Yan Xu, San Yang Liu (2017)
Open Mathematics
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The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).
I. Lahiri (1989)
Matematički Vesnik
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Pranay Goswami, Teodor Bulboacă, Rubayyi T. Alqahtani (2016)
Open Mathematics
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In this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.
Le Mau Hai, Nguyen Van Khue (1992)
Annales de l'institut Fourier
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The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.