Abstract
Let f be transcendental and meromorphic in the complex plane. In this article, we investigate the existences of zeros and fixed points of the linear combination and quotients of shifts of $f(z)$ when $f(z)$ is of order one. We also prove a result concerning the linear combination which extends a result of Bergweiler and Langley. Some results concerning the order of $f(z) <1$ are also obtained.
Highlights
Introduction and main resultsIn this article, a function is called meromorphic if it is analytic in the whole complex plane except at possible isolated poles
We assume that readers are familiar with the basic results and notations of the Nevanlinna value distribution theory of meromorphic functions
In Theorem D, Bergweiler and Langley considered the existence of zeros of first difference operator when the transcendental meromorphic function is of lower order less than one
Summary
Introduction and main resultsIn this article, a function is called meromorphic if it is analytic in the whole complex plane except at possible isolated poles. Theorem D Let f be a function transcendental and meromorphic of lower order λ(f ) < λ < in the plane.
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