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Fixed Point Theory and Applications

, 2010:417480

First Online: 18 October 2010Received: 17 August 2010Accepted: 15 October 2010

Abstract

A result of Hinchliffe 2003 is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let Open image in new window be an analytic function, Open image in new window a family of analytic functions in a domain Open image in new window, and Open image in new window a transcendental entire function. If Open image in new window and Open image in new window share Open image in new window IM for each pair Open image in new window, and one of the following conditions holds: 1 Open image in new window has at least two distinct zeros for any Open image in new window; 2 Open image in new window is nonconstant, and there exists Open image in new window such that Open image in new window has only one distinct zero Open image in new window, and suppose that the multiplicities Open image in new window and Open image in new window of zeros of Open image in new window and Open image in new window at Open image in new window, respectively, satisfy Open image in new window, for each Open image in new window, where Open image in new window; 3 there exists a Open image in new window such that Open image in new window has no zero, and Open image in new window is nonconstant, then Open image in new window is normal in Open image in new window.

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Autor: Qifeng Wu - Bing Xiao - Wenjun Yuan

Fuente: https://link.springer.com/







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