An application of fractional calculus to a new class of multivalent functions with negative coefficients. (English) Zbl 0940.30006

From the summary: Motivated by some earlier works of M.-P. Chen and H. M. Srivastava [Comput. Math. Appl. 35, No. 5, 83-91 (1998; Zbl 0921.30012)]; H. M. Srivastava and M. K. Aouf [J. Math. Anal. Appl. 171, 1-13 (1992; Zbl 0760.30006); ibid. f92, 673-688 (1995; Zbl 0831.30008)], dealing with various applications of the operators of fractional calculus in analytic function theory, the authors introduce and study rather systematically a certain subclass of analytic and \(p\)-valent functions with negative coefficients. This subclass is defined by using a familiar fractional derivative operator. Coefficient estimates, growth and distortion theorems, and many other interesting and useful properties and characteristics of this class of analytic and \(p\)-valent functions are obtained; some of these properties involve, for example, linear combinations and modified Hadamard products (or convolution) of functions belonging to the class introduced here.


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