Geodesic
On Janowski type harmonic functions associated with the Wright hypergeometric functions
Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 4, pp. 91-102

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In our present study we consider Janowski type harmonic functions class introduced and studied by Dziok, whose members are given by $h(z) = z + \sum_{n=2}^{\infty} h_n z^n$ and $g(z) = \sum_{n=1}^{\infty} g_n z^n$, such that $\mathcal{ST}_{H}(F,G)=\big\{ f = h + \bar{g} \in {H}:\frac{\mathfrak{D}_H f(z)}{f(z)}\prec\frac{1+Fz}{1+G z}; (-G \leq F G \leq 1, \text{ with } g_1=0)\big\},$ where $\mathfrak{D}_H f(z) = zh'(z)-\overline{zg'(z)} $ and $z\in \mathbb{U}=\{z:z\in \mathbb{C} \text{ and }|z| 1 \}.$ We investigate an association between these subclasses of harmonic univalent functions by applying certain convolution operator concerning Wright's generalized hypergeometric functions and several special cases are given as a corollary. Moreover we pointed out certain connections between Janowski-type harmonic functions class involving the generalized Mittag–Leffler functions. Relevant connections of the results presented herewith various well-known results are briefly indicated. 
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     author = {G. Murugusundaramoorthy and S. Porwal},
     title = {On {Janowski} type harmonic functions associated with the {Wright} hypergeometric functions},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {91--102},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2023_25_4_a8/}
}
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G. Murugusundaramoorthy; S. Porwal. On Janowski type harmonic functions associated with the Wright hypergeometric functions. Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 4, pp. 91-102. http://geodesic.mathdoc.fr/item/VMJ_2023_25_4_a8/