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Radii of starlikeness and convexity of generalized Mittag-Leffler functions

Arpad Baricz
Anuja Prajapati

Puni tekst: engleski, pdf (372 KB) str. 117-135 preuzimanja: 112* citiraj
APA 6th Edition
Baricz, A. i Prajapati, A. (2020). Radii of starlikeness and convexity of generalized Mittag-Leffler functions. Mathematical Communications, 25 (1), 117-135. Preuzeto s https://hrcak.srce.hr/235561
MLA 8th Edition
Baricz, Arpad i Anuja Prajapati. "Radii of starlikeness and convexity of generalized Mittag-Leffler functions." Mathematical Communications, vol. 25, br. 1, 2020, str. 117-135. https://hrcak.srce.hr/235561. Citirano 16.04.2021.
Chicago 17th Edition
Baricz, Arpad i Anuja Prajapati. "Radii of starlikeness and convexity of generalized Mittag-Leffler functions." Mathematical Communications 25, br. 1 (2020): 117-135. https://hrcak.srce.hr/235561
Harvard
Baricz, A., i Prajapati, A. (2020). 'Radii of starlikeness and convexity of generalized Mittag-Leffler functions', Mathematical Communications, 25(1), str. 117-135. Preuzeto s: https://hrcak.srce.hr/235561 (Datum pristupa: 16.04.2021.)
Vancouver
Baricz A, Prajapati A. Radii of starlikeness and convexity of generalized Mittag-Leffler functions. Mathematical Communications [Internet]. 2020 [pristupljeno 16.04.2021.];25(1):117-135. Dostupno na: https://hrcak.srce.hr/235561
IEEE
A. Baricz i A. Prajapati, "Radii of starlikeness and convexity of generalized Mittag-Leffler functions", Mathematical Communications, vol.25, br. 1, str. 117-135, 2020. [Online]. Dostupno na: https://hrcak.srce.hr/235561. [Citirano: 16.04.2021.]

Sažetak
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-P\'{o}lya 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, Ostrovski\u{i} 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.

Ključne riječi
Generalized Mittag-Leffler functions; starlike and convex functions; radius of starlikeness; radius of convexity; entire functions; real zeros; Euler-Rayleigh inequalities; Weierstrassian decomposition

Hrčak ID: 235561

URI
https://hrcak.srce.hr/235561

Posjeta: 192 *