Abstract
In this paper we consider the question of the existence of fixed points of the derivatives of solutions of complex linear differential equations in the unit disc. This work improves some very recent results of T.-B. Cao.
Highlights
Introduction and main resultsIn this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s theory on the complex plane and in the unit disc D = {z ∈ C : |z| < 1}
We assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s theory on the complex plane and in the unit disc D = {z ∈ C : |z| < 1}
Many important results have been obtained on the fixed points of general transcendental meromorphic functions for almost four decades, see [4]
Summary
There are few studies on the fixed points of solutions of differential equations, specially in the unit disc. Cao [1] firstly investigated the fixed points of solutions of linear complex differential equations in the unit disc. For n ∈ N, the iterated n-convergence exponent of the sequence of fixed points in D of a meromorphic function f in D is defined by τn(f. Λn(f − z), the iterated n-convergence exponent of the sequence of distinct fixed points in D of a meromorphic function f in D is defined by τ n(f. Cao investigated the fast growth of the solutions of high order complex differential linear equation with analytic coefficients of n-iterated order in the unit disc.
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