Tomovski, Ž., Gerhold, S., Bansal, D., & Soni, A. (2022). Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk. Axioms, 11(10), Article 568. https://doi.org/10.3390/axioms11100568
E105 - Institut für Stochastik und Wirtschaftsmathematik
-
Zeitschrift:
Axioms
-
ISSN:
2075-1680
-
Datum (veröffentlicht):
2022
-
Umfang:
13
-
Verlag:
MDPI
-
Peer Reviewed:
Ja
-
Keywords:
close-to-convex function; generalized Mathieu-type series; starlike function; univalent function
en
Abstract:
We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients. Using criteria due to Fejér and Ozaki, we provide sufficient conditions for these functions to be close-to-convex or starlike inside the unit disk, and thus univalent. One of our proofs is assisted by symbolic computation.
