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Geometric properties of some generalized Mathieu power series inside the unit disk

Complex Variables 2021-09-09 v1

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 Fejer and Ozaki, we provide sufficient conditions for these functions to be close-to-convex or starlike inside the unit disk, and thus univalent.

Keywords

Cite

@article{arxiv.2109.03657,
  title  = {Geometric properties of some generalized Mathieu power series inside the unit disk},
  author = {Stefan Gerhold and Zivorad Tomovski and Deepak Bansal and Amit Soni},
  journal= {arXiv preprint arXiv:2109.03657},
  year   = {2021}
}