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DOI: 10.46698/b2503-7977-9793-e

On Janowski Type Harmonic Functions Associated with the Wright Hypergeometric Functions

Murugusundaramoorthy, G. , Porwal, S.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 4.
Abstract:
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.
Keywords: harmonic functions, univalent functions, Wright's generalized hypergeometric functions
Language: English Download the full text  
For citation: Murugusundaramoorthy, G. and Porwal, S. On Janowski Type Harmonic Functions Associated with the Wright Hypergeometric Functions, Vladikavkaz Math. J., 2023, vol. 25, no. 4, pp. 91-102. DOI 10.46698/b2503-7977-9793-e
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