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Afrika Matematika

, Volume 29, Issue 3–4, pp 625–639 | Cite as

Iterated exponent of convergence of solutions of linear differential equations in the unit disc

  • H. Fettouch
  • S. Hamouda
Article

Abstract

In this paper we investigate the n-iterated exponent of convergence of \( f^{\left( i\right) }-\varphi \) where \(f\not \equiv 0\) is a solution of linear differential equation with analytic and meromorphic coefficients in the unit disc and \(\varphi \) is a small function of f. By this investigation we can deduce the value distribution of the fixed points of \(f^{\left( i\right) }\) by taking \(\varphi \left( z\right) =z\). This work is an extension to the unit disc and an improvement of recent results in the complex plane by Xu et al. (Adv Differ Equ 2012(114):1–16, 2012) and Tu et al. (Adv Differ Equ 2013(71):1–16, 2013).

Keywords

Linear differential equations Exponent of convergence Growth of solutions Unit disc 

Mathematics Subject Classification

34M10 30D35 

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Pure and Applied MathematicsUMAB University of MostaganemMostaganemAlgeria

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