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Basic properties and characterizations of a certain class of analytic functions with negative coefficients. II. (English) Zbl 0826.30007

Summary: [For part I see Sang Keun Lee and S. Owa and H. M. Srivastava in Util. Math. 36, 121-128 (1989; Zbl 0639.30009).]
The object of the present paper is to determine the closure theorems of the class \(F_p (\lambda, \alpha)\) consisting of certain analytic functions with negative coefficients in the unit disc. Also we obtain radii of close-to-convexity, starlikeness and convexity for the class \(F_p (\lambda, \alpha)\). Furthermore, distortion theorems for fractional calculus are shown. Also modified Hadamard products of several functions belonging to the class \(F_p (\lambda, \alpha)\) are studied here.

MSC:

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

Citations:

Zbl 0639.30009
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