Fekete-Szegö inequality for certain class of Bazilevic functions. (English) Zbl 1073.30011

Summary: In this present investigation, the authors obtain a Fekete-Szegö inequality for certain normalized analytic function \(f(z)\) defined on the open unit disk for which \(z^{1-\alpha}f'(z)/f^{1-\alpha}(z) (\alpha\geq 0)\) lies in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain application of the main result for a class of functions defined by convolution is given. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through fractional derivatives is obtained.


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