Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk

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 co...

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Bibliographic Details
Published inAxioms Vol. 11; no. 10; p. 568
Main Authors Tomovski, Živorad, Gerhold, Stefan, Bansal, Deepak, Soni, Amit
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2022
Subjects
close-to-convex function
Factorials
generalized Mathieu-type series
Mathematical research
Power series
Series
starlike function
univalent function
Czech Republic
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11100568