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Journal of Complex Analysis
Volume 2017, Article ID 3253095, 10 pages
https://doi.org/10.1155/2017/3253095
Research Article

Entire Functions of Bounded L-Index: Its Zeros and Behavior of Partial Logarithmic Derivatives

1Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska St., Ivano-Frankivsk 76019, Ukraine
2Department of Function Theory and Theory of Probability, Ivan Franko National University of Lviv, 1 Universytetska St, Lviv 79000, Ukraine

Correspondence should be addressed to Andriy Bandura; moc.liamg@aistynapokyirdna

Received 5 August 2017; Accepted 15 October 2017; Published 6 November 2017

Academic Editor: Stanislawa Kanas

Copyright © 2017 Andriy Bandura and Oleh Skaskiv. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we obtain new sufficient conditions of boundedness of -index in joint variables for entire function in functions. They give an estimate of maximum modulus of an entire function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives and the distribution of zeros. In some sense, the obtained results are new for entire functions of bounded index and -index in too. They generalize known results of Fricke, Sheremeta, and Kuzyk.