Geodesic
A class of harmonic $(p,q)$-starlike functions involving a generalized $(p,q)$-Bernardi integral operator
Problemy analiza, Tome 12 (2023) no. 2, pp. 17-36

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With the aid of $q$-calculus, this paper introduces a new generalized $(p, q)$-Bernardi integral operator $\mathcal{B}_{n,q}^{p}f(z)$. Then, we define a new subclass of harmonic $(p, q)$-starlike functions of complex order associated with the operator $\mathcal{B}_{n,q}^{p}f(z)$. For this new subclass, a necessary and sufficient condition, compact and convex combination theorems, a distortion theorem, and extreme points are investigated. Finally, we discuss the weight mean theorem for functions belonging to this class. This research highlights the significant connections between the results presented in this study and previous works.
Keywords: harmonic functions, q)$-Bernardi integral operator, distortion bounds, extreme points, convex combination.
Mots-clés : $q$-calculus, $(p 
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     title = {A class of harmonic $(p,q)$-starlike functions involving a generalized $(p,q)${-Bernardi} integral operator},
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     url = {http://geodesic.mathdoc.fr/item/PA_2023_12_2_a1/}
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S. H. Hadi; M. Darus. A class of harmonic $(p,q)$-starlike functions involving a generalized $(p,q)$-Bernardi integral operator. Problemy analiza, Tome 12 (2023) no. 2, pp. 17-36. http://geodesic.mathdoc.fr/item/PA_2023_12_2_a1/