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Coefficient estimates for subclasses of analytic functions related to Bernoulli's lemniscate and an application of Poisson distribution series | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 23، دوره 13، شماره 2، مهر 2022، صفحه 237-251 اصل مقاله (566.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.21296.2244 | ||
| نویسندگان | ||
| Murugusundaramoorthy Gangadharan* 1؛ Teodor Bulboacă2 | ||
| 1Department of Mathematics, SAS, Vellore Institute of Technology, deemed to be University, Vellore-632014, India | ||
| 2Faculty of Mathematics and Computer Science, Babes-Bolyai University, 400084 Cluj-Napoca, Romania | ||
| تاریخ دریافت: 16 تیر 1399، تاریخ بازنگری: 16 شهریور 1399، تاریخ پذیرش: 23 شهریور 1399 | ||
| چکیده | ||
| Using the $q$-calculus operator we defined a new subclass of analytic functions $\mathcal{M}_q(\vartheta,\Phi)$ defined in the open unit disk $\Delta=\{z\in\mathbb{C}:\left\vert z\right\vert<1\}$ related with Bernoulli's lemniscate and obtained certain coefficient estimates, Fekete-Szeg\H{o} inequality results for $f\in\mathcal{M}_q(\vartheta,\Phi)$. As a special case of our result, we obtain Fekete-Szeg\H{o} inequality for a class of functions defined through Poisson distribution and further with the help of MAPLE\texttrademark\ software we find Hankel determinant inequality for $f\in\mathcal{M}_q(\vartheta,\Phi)$. Our investigation generalises some previous results obtained in different articles. | ||
| کلیدواژهها | ||
| Analytic functions؛ differential subordination؛ Fekete-SzegHo problem؛ $q-$calculus operator؛ Bernoulli's lemniscate | ||
| مراجع | ||
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