Abstract
In the present paper we start consideration of a new type problem in the theory of meromorphic functions ω. It turns out that any set of finite polygons which are far from each other, has many ω −1-preimages whose geometric shapes are quite similar to the shapes of initial polynomials. The obtained results have generalized one of versions of so called proximity property which describes geometric locations of simple a-points and, in turn, implies the main conclusions of classical value distribution theory describing these points only quantitatively. The newly obtained properties can be used to study meromorphic functions ω whose a-points lie on finite non-parallel lines for a belonging to a given set.
The work was supported by the UGC grant of Hong Kong, Project No. 6134/00P HKUST
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barsegian, G.: On the geometry of meromorphic functions, Math. Sbornic, 114(156), no. 2 (1981), 179–226. (in Russian)
Barsegian, G.: On the geometry of meromorphic functions, Math. Sbornic, Math. USSR Sbornic 42, no. 2 (1982), 155–196.
Barsegian, G.: A proximity property of the a-points of meromorphic functions. Math. Sbornic, 120 (162) (1983), 42–63 (in Russian)
Barsegian, G.: A proximity property of the a-points of meromorphic functions. Math. USSR Sbornik 48 (1984), 41–63.
Barsegian, G.A., Yang C.C.: Some new generalizations in the theory of meromorphic functions and their applications. Part 1. On the magnitudes of functions on the sets of a-points of derivatives, Complex Variables, Theory Appl. 41 (2000), 293–313.
Barsegian, G.A., Yang C.C.: Some new generalizations in the theory of meromorphic functions and their applications. Part 2. On the derivatives of meromorphic and inverse functions. Complex Variables, Theory Appl. 44 (2001), 13–28.
Nevanlinna, R.: Eindeutige analytische Funktionen. Springer, Berlin, 1936.
Ozawa, M.: On the solution of the functional equation f og(z) = F(z). Y. Kodai Math. Sem. Rep. 20 (1968), 305–313.
Baker, I.N.: Entire functions whose A-points lie on a system of lines. Lectutre Notes in Pure and Applied Mathematics 78, Marcel Dekker 1982, 1–186.
Golusin, G.M.: Geometric function theory of complex variables. Nauka, Moscow 1966 (in Russian).
Hayman, W.K.: Multivalent functions. Cambridge University Press 1958.
Qiao, J.: Factorizations of meromorphic functions. Chinese Annals of Math. 10A (1989) 692–698 (in Chinese).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Barsegian, G.A., Yang, C.C. (2003). A New Property of Meromorphic Functions and Its Applications. In: Begehr, H.G.W., Gilbert, R.P., Wong, M.W. (eds) Analysis and Applications — ISAAC 2001. International Society for Analysis, Applications and Computation, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3741-7_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3741-7_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5247-9
Online ISBN: 978-1-4757-3741-7
eBook Packages: Springer Book Archive