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This article is cited in 5 scientific papers (total in 5 papers)
A class of harmonic $(p,q)$-starlike functions involving a generalized $(p,q)$-Bernardi integral operator
S. H. Hadiab, M. Darusb a Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
b Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia
Abstract:
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, $q$-calculus, $(p, q)$-Bernardi integral operator, distortion bounds, extreme points, convex combination.
Received: 11.12.2022 Revised: 07.03.2023 Accepted: 06.03.2023
Citation:
S. H. Hadi, M. Darus, “A class of harmonic $(p,q)$-starlike functions involving a generalized $(p,q)$-Bernardi integral operator”, Probl. Anal. Issues Anal., 12(30):2 (2023), 17–36
Linking options:
https://www.mathnet.ru/eng/pa373 https://www.mathnet.ru/eng/pa/v30/i2/p17
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Abstract page: | 96 | Full-text PDF : | 38 | References: | 24 |
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