1. Radii of starlikeness and convexity of generalized Mittag-Leffler functions.
- Author
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BARICZ, ÁRPÁD and PRAJAPATI, ANUJA
- Subjects
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THEORY of distributions (Functional analysis) , *STAR-like functions , *ANALYTIC functions , *RADIUS (Geometry) , *INTEGRAL functions , *CONVEX functions - Abstract
In this paper our aim is to find the radii of starlikeness and convexity of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-Pólya class and a result of H. Kumar and M.A. Pathan on the reality of the zeros of generalized Mittag-Leffler functions, which origins goes back to Dzhrbashyan, Ostrovskiĭ and Peresyolkova, play important roles in this paper. Moreover, the interlacing properties of the zeros of Mittag-Leffler function and its derivative is also useful in the proof of the main results. By using the Euler-Rayleigh inequalities for the real zeros of the generalized Mittag-Leffler function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero. [ABSTRACT FROM AUTHOR]
- Published
- 2020