On characteristic of bounded analytic functions involving hyperbolic derivative
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Nan Wu
Abstract
In this article, we give the Nevanlinna type hyperbolic characteristics in simply connected domains and angular domains and the Tsuji type hyperbolic characteristics for bounded analytic functions for the first time. The first fundamental theorems are also established concerning hyperbolic derivative for bounded analytic functions in simply connected domains and angular domains. This is a continuous work of Makhmutov [3].
Communicated by Stanisława Kanas
Acknowledgement
The author is supported by grants (No.11231009, 11371363, 11501563, 11571049) of NSFC of China and Yue Qi Young Scholar Program, China University of Mining and Technology, Beijing.
References
[1] Goldberg, A. A.—Ostrovskii, I. V.: The distribution of values of meromorphic functions (in Russian), Izdat. Nauk. Moscow, 1970. English translation by Mikhail Ostrovskii, Transl. Math. Monogr. 236, American Mathematical Society, Providence, RI, 2008.Search in Google Scholar
[2] Hayman W. K.: Meromorphic Functions, Oxford, 1964.Search in Google Scholar
[3] Makhmutov, S.: Value distribution of bounded analytic functions, New Zealand J. Math. 39 (2009), 19–24.Search in Google Scholar
[4] Tsuji, M.: Potential Theory in Modern Function Theory, Maruzen Co., LTD Tokyo, 1959.Search in Google Scholar
[5] Zheng, J. H.: Value Distribution of Meromorphic Functions, Tsinghua University Press and Springer-Verlag, Beijing and Berlin, 2010.Search in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A multi-parameter generalization of the symmetric algorithm
- Single identities forcing lattices to be Boolean
- Weighted uniform density ideals
- A generalized class of restricted Stirling and Lah numbers
- The Riemann hypothesis and universality of the Riemann zeta-function
- Distance functions on the sets of ordinary elliptic curves in short Weierstrass form over finite fields of characteristic three
- The drazin inverse of the sum of two matrices
- Refinements of the majorization-type inequalities via green and fink identities and related results
- Characterizations and properties of graphs of Baire functions
- Some improvements of the young mean inequality and its reverse
- On characteristic of bounded analytic functions involving hyperbolic derivative
- A uniqueness problem for entire functions related to Brück’s conjecture
- System of nonlocal resonant boundary value problems involving p-Laplacian
- Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
- Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces
- Characterization of rough weighted statistical limit set
- Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers
- On generalized 4-th root metrics of isotropic scalar curvature
- Compactifications from generators and relations
- Diophantine quadruples with values in k-generalized Fibonacci numbers
