Harmonic spirallike functions and harmonic strongly starlike functions

Xiu-Shuang Ma; Saminathan Ponnusamy; Toshiyuki Sugawa

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arXiv · 2108.11622

Harmonic spirallike functions and harmonic strongly starlike functions

Xiu-Shuang Ma·Saminathan Ponnusamy·Toshiyuki Sugawa

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Abstract

Harmonic functions are natural generalizations of conformal mappings. In recent years, a lot of work have been done by some researchers who focus on harmonic starlike functions. In this paper, we aim to introduce two classes of harmonic univalent functions of the unit disk, called hereditarily $\lambda$-spirallike functions and hereditarily strongly starlike functions, which are the generalizations of $\lambda$-spirallike functions and strongly starlike functions, respectively. We note that a relation can be obtained between this two classes. We also investigate analytic characterization of hereditarily spirallike functions and uniform boundedness of hereditarily strongly starlike functions. Some coefficient conditions are given for hereditary strong starlikeness and hereditary spirallikeness. As a simple application, we consider a special form of harmonic functions.

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BibTeX RIS

Xiu-Shuang Ma, Saminathan Ponnusamy, Toshiyuki Sugawa. 2021-08-26. Harmonic spirallike functions and harmonic strongly starlike functions. https://arxiv.org/abs/2108.11622

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