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

被引：1

作者：

Tomovski, Zivorad ^{[1
,2
]}

Gerhold, Stefan ^{[3
]}

Bansal, Deepak ^{[4
]}

Soni, Amit ^{[5
]}

机构：

[1] Univ Ostrava, Fac Sci, Dept Math, Ostrava 70103, Czech Republic

[2] Ss Cyril & Methodius Univ, Fac Math & Nat Sci, Dept Math, Skopje 1000, North Macedonia

[3] Tech Univ Wien, Inst Stat & Math Methods Econ, A-1040 Vienna, Austria

[4] Univ Coll Engn & Technol, Dept Math, Bikaner 334004, India

[5] Govt Engn Coll, Dept Math, Bikaner 334004, India

来源：

AXIOMS | 2022年 / 11卷 / 10期

关键词：

univalent function; starlike function; close-to-convex function; generalized Mathieu-type series; HYPERGEOMETRIC-FUNCTIONS; FAMILIES;

D O I：

10.3390/axioms11100568

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Fejer 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.

引用

页数：13

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