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A class of \(\alpha\)-uniformly univalent analytic functions involving differentio-integral operator. (English) Zbl 1291.30078

Summary: Let \(T_{\delta}US^*(I^{m},\alpha,\beta,z_{0})\) and \(T_{\delta}UC(I^{m},\alpha,\beta,z_{0})\) denote, repectively, the classes of univalent analytic functions having negative coefficients with two fixed points which are \(\alpha\)-uniformly starlike functions of order \(\beta\) and \(\alpha\)-uniformly convex functions of order \(\beta\) involving differentio-integral operator. We determine the coefficent inequalities, distortion theorems, extreme points, integral representaton and radii of starlikeness and convexity for these classes.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C55 General theory of univalent and multivalent functions of one complex variable
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