## Some applications of differential subordination.(English)Zbl 0575.30018

Using the techniques of differential subordination developed by P. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade [General inequalities 3, 3rd int. Conf., Oberwolfach 1981, ISNM 64, 339-348 (1983; Zbl 0527.30008)] the authors show that if f(z) is in a certain class of regular functions, then so is $F(z)=((c+1)/c)\int^{z}_{0}t^{c-1}f(t)dt.$ The function f(z) must satisfy a subordination condition. The authors’ work generalizes and combines prior similar results of, for example, the reviewer [Proc. Am. Math. Soc. 16, 755-758 (1965; Zbl 0158.077)], St. Ruscheweyh [Proc. Am. Math. Soc. 49, 109-115 (1975; Zbl 0303.30006)], etc.
Reviewer: R.Libera

### MSC:

 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

### Keywords:

differential subordination

### Citations:

Zbl 0527.30008; Zbl 0158.077; Zbl 0303.30006
Full Text:

### References:

 [1] Goel, Indian J. Pure. Appl. Math. 12 pp 1240– (1981) [2] Eenigenburg, On a Briot. Bouquet differential subordination 3 pp 339– (1983) [3] DOI: 10.2307/2041942 · Zbl 0355.30013 [4] Hassoon, Rev. Roum. Math. Pures et Appl. 23 pp 1449– (1978) [5] DOI: 10.1307/mmj/1028988895 · Zbl 0048.31101 [6] DOI: 10.2307/2039801 · Zbl 0303.30006 [7] DOI: 10.2307/2039483 · Zbl 0258.30012 [8] DOI: 10.2307/2033917 · Zbl 0158.07702 [9] Zmorovich, Ukrain. Mat. 33 pp 670– (1981)
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