More on convex functions of bounded type

Goodman, A. W.

doi:10.1090/S0002-9939-1986-0835886-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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More on convex functions of bounded type
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by A. W. Goodman PDF

Proc. Amer. Math. Soc. 97 (1986), 303-306 Request permission

Abstract:

A normalized univalent function is convex of bounded type if the curvature of the curve bounding the image domain lies between two fixed positive numbers. In this work we find sharp bounds for the modulus of the function and its derivative. We also discuss the coefficient problem for this new class of functions.

References

A. W. Goodman, Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983. MR 704183
A. W. Goodman, Convex functions of bounded type, Proc. Amer. Math. Soc. 92 (1984), no. 4, 541–546. MR 760942, DOI 10.1090/S0002-9939-1984-0760942-5
A. W. Goodman, Convex curves of bounded type, Internat. J. Math. Math. Sci. 8 (1985), no. 4, 625–633. MR 821617, DOI 10.1155/S0161171285000680