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On the maximal terms of succesive Gelfond-Leont’ev-Salagen and Gelfond-
Leont’ev-Ruscheweyh derivatives of a function analytic in the unit disc |
| Author |
M. M. Sheremeta
m_m_sheremeta@list.ru
Ivan Franko National University of Lviv
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| Abstract |
For a function analytic in the unit disc the concepts of Gelfond-Leont'ev-Salagen and
Gelfond-Leont'ev-Ruscheweyh derivatives of n-th 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 Gelfond-Leont’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)
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| Pages |
58-64 |
| Volume |
37 |
| Issue |
1 |
| Year |
2012 |
Journal |
Matematychni Studii |
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