Ostrovskii, I. V.Üreyen, A. E.2016-02-082016-02-0820060016-2663http://hdl.handle.net/11693/23710We show that entire transcendental functions f satisfying log M(r,f) = o(log 2r), r → ∞ (M(r,f): = maxf(z)| necessarily have growth irregularity, which increases as the growth diminishes. In particular, if 1 < p < 2, then the asymptotics log M(r,f) = (log pr) +0 (log2-pr), r → ∞ is impossible. It becomes possible if "o" is replaced by "O.". © Springer Science+Business Media, Inc. 2006.EnglishClunie - Kövari theoremErdös - Kövari theoremHayman convexity theoremLevin ' s strong proximate orderMaximum termArticle10.1007/s10688-006-0047-71573-8485