On a certain class of harmonic functions and the generalized Bernardi-Libera-Livingston integral operator

Grigore Stefan Salagean, Pall-Szabo Agnes Orsolya

Abstract


In this paper we examine the closure properties of the class $\mathcal{V}_\mathcal{H}(F;\gamma)$ under the generalized Bernardi-Libera-Livingston integral \\operator $\mathcal{L}_{c}(f),$ ($c>-1$) which is defined by
$ \mathcal{L}_{c}(f)=\mathcal{L}_{c}(h)+\overline{\mathcal{L}_{c}(g)}$ where
\begin{equation*}
\mathcal{L}_{c}(h)(z)=\frac{c+1}{z^{c}}\int\limits_{0}^{z}(t^{c-1}h(t) dt \;\;\;%
\mathrm{and} \;\;\; \mathcal{L}_{c}(g)(z)=\frac{c+1}{z^{c}}\int\limits_{0}^{z}(t^{c-1}g(t) dt.
\end{equation*}
The obtained results are sharp and they improve known results.


Keywords


harmonic univalent functions; extreme points

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2020.3.05

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