On the univalence of a certain integral-Reference-Cited by-同舟云学术

On the univalence of a certain integral

Published:1971 Issue:1 Volume:27 Page:97-100
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Merkes E. P.,Wright D. J.

Abstract

We consider the function g ( z ) = ∫ 0 z [ f ( t ) / t ] α d t g(z) = \smallint _0^z{[f(t)/t]^\alpha }dt for f f in the classes of convex, starlike, and close-to-convex univalent functions, and we determine precisely which values of α \alpha yield a close-to-convex function g g .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-027-01/S0002-9939-1971-0269825-1/S0002-9939-1971-0269825-1.pdf

Reference6 articles.

1. The close-to-convexity and univalence of an integral;Causey, W. M.;Math. Z.,1967

2. Close-to-convex schlicht functions;Kaplan, Wilfred;Michigan Math. J.,1952

3. A. Marx, Untersuchungen über schlichte Abbildungen, Math. Ann. 107 (1932), 40-67.

4. On the univalence of a certain integral;Nunokawa, Mamoru;Trans. Amer. Math. Soc.,1969

5. On the univalence of a certain integral;Royster, W. C.;Michigan Math. J.,1965

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