Bounded l-index and l-M-index and compositions of analytic functions
Journal Title: Математичні Студії - Year 2017, Vol 48, Issue 2
Abstract
We partially proved a conjecture from Mat. Stud. 47 (2017), no.2, 207--210: for an entire function f the function H(z)=f(1/(1−z)n), n∈N, is of bounded l-index in C∖{0} with l(|z|)=β/(1−|z|)n+1, β>1, if and only if f is of bounded index. Also the boundedness of l-M-index of the function H is investigated. For arbitrary entire functions f and g the boundedness of the l-M-index of the function F(z)=f(g(z)) is studied with respect to boundedness of the M-index of a function f with l(r)=M′g(r), Mg(r)=max{|g(z)|:|z|=r}.
Authors and Affiliations
Andriy Bandura, Myroslav Sheremeta
Keywords
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- EP ID EP302543
- DOI 10.15330/ms.48.2.180-188
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