
On the maximal terms of succesive GelfondLeont’evSalagen and Gelfond
Leont’evRuscheweyh derivatives of a function analytic in the unit disc 
Author 
M. M. Sheremeta
m_m_sheremeta@list.ru
Ivan Franko National University of Lviv

Abstract 
For a function analytic in the unit disc the concepts of GelfondLeont'evSalagen and
GelfondLeont'evRuscheweyh derivatives of nth order are introduced and the asymptotic
behaviour of the maximal terms of their power development as $n\to+\infty$ is investigated. 
Keywords 
analytic function; derivatives of GelfondLeont’ev; Salagen and Rusheweyh; maximal term of
power series 
Reference 
1. Gelfond A.O., Leont’ev A.F. On a generalisation of Fourier series// Matem. Sb. – 1951. – V.29, ¹3. –
P. 477–500. (in Russian)
2. Salagean G.St. Subclasses of univalent functions// Lecture Notes in Math. – 1983. – V.1013. – P. 362–372.
3. Ruscheweyh St. New criteria for univalent functions// Proc. Amer. Math. Soc. – 1975. – V.49. – P. 109–
115.
4. Zabolotskyi M.V., Sheremeta M.M. A generalisation of Lindel.off theorem// Ukr. Mat. Zh. – 1998. – V.50,
¹9. – P. 1177–1192. (in Ukrainian)

Pages 
5864 
Volume 
37 
Issue 
1 
Year 
2012 
Journal 
Matematychni Studii 
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