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A note on certain classes of starlike functions. (English) Zbl 0596.30018
A number of distortion theorems are proved for the classes \({\mathcal T}_{\alpha}(n)\) and \({\mathcal C}_{\alpha}(n)\) of analytic and univalent functions with negative coefficients, studied recently by S. K. Chatterjea [J. Pure Math. 1, 23-26 (1981; Zbl 0514.30010)]. Several interesting results for the convolution product of functions belonging to the classes \({\mathcal T}_{\alpha}(n)\) and \({\mathcal C}_{\alpha}(n)\) are also presented rather systematically.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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References:
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