Geodesic
An Inequality Concerning Analytic Functions with a Positive Real Part
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1172-1177

Voir la notice de l'article provenant de la source Cambridge University Press

This paper contains an inequality about functions which are analytic and have a positive real part in the unit disk. A first consequence of the inequality is the fact that if is analytic for |z| < 1 and has values lying in a strip of width δ. This result is known and was first proved by Tammi (1).Our second theorem is a generalization of this. Namely, ifis analytic for |z| < 1 and satisfies Re{zmf(m>(z)} ≧ A and thenconverges.Another application of our fundamental inequality is the following. Let be analytic for |z| < 1 and satisfy Re p(z) ≧ 0 and set and . 
MacGregor, Thomas H. An Inequality Concerning Analytic Functions with a Positive Real Part. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1172-1177. doi: 10.4153/CJM-1969-128-0
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[1] 1. Tammi, O., Note on Gutzmer's coefficient theorem, Rev. Fac. Sci. Univ. Istanbul Sér. A 22 (1957), 9–12. Google Scholar

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