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Authors: GRIGORE ȘTEFAN SĂLĂGEAN, ÁGNES ORSOLYA PÁLL-SZABÓ.
DOI: 10.24193/subbmath.2020.3.05
Published Online: 2020-09-15
Published Print: 2020-09-15
pp. 365-371
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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 egin{equation*} mathcal{L}_{c}(h)(z)=frac{c+1}{z^{c}}intlimits_{0}^{z}(t^{c-1}h(t) dt ;;;% mathrm{and} ;;; mathcal{L}_{c}(g)(z)=frac{c+1}{z^{c}}intlimits_{0}^{z}(t^{c-1}g(t) dt. end{equation*} The obtained results are sharp and they improve known results.
Key words: harmonic univalent functions; extreme points
