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http://dx.doi.org/10.14317/jami.2011.29.1_2.451

MAXIMUM CURVES OF TRANSCENDENTAL ENTIRE FUNCTIONS OF THE FORM $E^{p(z)}$  

Kim, Jeong-Heon (Department of Mathematics, Soongsil University)
Kim, Youn-Ouck (Soongsil University)
Kim, Mi-Hwa (Soongsil University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 451-457 More about this Journal
Abstract
The function f(z) = $e^{p(z)}$ where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of $e^{p(z)}$ divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, $e^{p(z)}$ has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of $e^{p(z)}$. We deal with some properties of maximum curves of $e^{p(z)}$ and we give some examples of the maximum curves of functions of the form $e^{p(z)}$.
Keywords
Radial limit; Julia line; maximum modulus function; maximum curve; isolated maximum point;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 T. F. Tyler, Maximum curves and isolated points of entire functions, Proc. of the Amer. Math. Soc. 128(2000)9, 2561-2568.   DOI   ScienceOn
2 J. M. Anderson, K. F. Barth and D. A. Brannan,Research problems in complex analysis, Bull. London math. Soc. 9 (1977), 129-162.   DOI
3 C. T. Chuang, Normal Families of Meromorphic Functions, World Scientific, Singapore, 1993.
4 D. Gaier, Lectures on Complex approximation, Birkhauser, Boston, 1987.
5 G. Julia, Lecons sur les fonctions uniformes a Point singulier essentiel Isole, Imprimerie Gauthier-Villar, Paris, 1924.
6 J. -H. Kim, K. H. Kwon and S. B. Park, On the normality of translated families of transcendental entire functions, J. of Appl. Math and Comp. 17(2005), 573-583.
7 A. I. Markushevich (trans. and ed. by R. A. Silverman), Theory and Functions of a Complex Variable, Chelsea Publ. Co., New York, 1977.