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Convex and starlike criteria

Herb Silverman

International Journal of Mathematics and Mathematical Sciences · 1999 · 80 citations · 6 references

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Abstract

We investigate an expression involving the quotient of the analytic representations of convex and starlike functions. Sufficient conditions are found for functions to be starlike of a positive order and convex.

References

6

Functions Starlike and Convex of Order α

I. S. Jack · Journal of the London Mathematical Society · 1971 · 492 citations

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Convex hulls and extreme points of families of starlike and convex mappings

Louis Brickman, D. J. Hallenbeck, Thomas H. MacGregor et al. · Transactions of the American Mathematical Society · 1973 · 85 citations · Full text

, , +14

The radius of convexity for starlike functions of order 1\over2

Thomas H. MacGregor · Proceedings of the American Mathematical Society · 1963 · 61 citations · Full text

, , +7

All $\alpha $-convex functions are univalent and starlike

Sanford S. Miller, Petru T. Mocanu, Maxwell O. Reade · Proceedings of the American Mathematical Society · 1973 · 59 citations · Full text

, , +4

Convex Hulls and Extreme Points of Families of Starlike and Convex Mappings

L. Brickman, D. J. Hallenbeck, Thomas H. MacGregor et al. · Transactions of the American Mathematical Society · 1973 · 43 citations

, , +14