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
Ivan Franko National University of Lviv

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
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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 58-64
Volume 37
Issue 1
Year 2012
Journal Matematychni Studii
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