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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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[1] C. Carath´eodory, Uber den Variabilit¨atsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo (2) 32 (1911), 193–217. [2] P.L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften, 259, Springer-Verlag, New York, USA, 1983. [3] M. Fekete and G. Szeg˝o, Eine Bemerkung ¨uber ungerade schlichte Funktionen, J. Lond. Math. Soc. (2) 8 (1933), 85–89. [4] M. E. H. Ismail, E. Merkes and D. Styer, A generalization of starlike functions, Complex Var. Theory Appl. 14 (1990), no. 1-4, 77–84. [5] F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edin. 46 (1908), 253–281. [6] F.R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12. [7] W. Koepf, On the Fekete-Szeg˝o problem for close-to-convex functions, Proc. Amer. Math. Soc. 101 (1987), no. 1, 89–95. [8] W. Koepf, On the Fekete-Szego problem for close-to-convex functions-II, Arch. Math. (Basel) 49 (1987), 420–433. [9] R.J. Libera and E.J. Zlotkiewicz, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc. 85 (1982), no. 2, 225–230. [10] R.J. Libera and E.J. Zlotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (1983), no. 2, 251–257. [11] W.C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Z. Li, F. Ren, L. Yang and S. Zhang (Eds.), Int. Press, Cambridge, MA, (1994), 157–169. [12] T.H. MacGregor, Functions whose derivative have a positive real part, Trans. Amer. Math. Soc. 104 (1962), no. 3, 532–537. [13] G. Murugusundaramoorthy, Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat. 28 (2017), 1357–1366. [14] G. Murugusundaramoorthy, K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacet. J. Math. Stat. 45 (2016), no. 4, 1101–1107. [15] K. Nazar, M. Shafiq, M. Darus, B.K. Qazai, A. Zahoor, Upper bound of the third Hankel determinant for a subclass of q–starlike functions associated with the lemniscate of Bernoulli, J. Math. Ineq. 14 (2020), no. 1, 53-–65. [16] Ch. Pommerenke, Univalent Functions, Vanderhoeck & Ruprecht, G¨ottingen, 1975. [17] S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. (2014), Art. ID 984135, 1–3. [18] S. Porwal and M. Kumar, A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat. 27 (2016), no. 5, 1021–1027. [19] M. Raza and S. Malik, Upper bound of third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, J. Inequal. Appl. 2013:412, (2013), 1–8. [20] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), no. 1, 109–115. [21] A.K. Sahoo and J. Patel, Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, Int. J. Anal. Appl. 6 (2014), no. 2, 170–177. [22] J. Sokol, Coefficient estimates in a class of strongly starlike functions, Kyungpook Math. J. 49 (2009), no. 2, 349–353. [23] J. Sokol and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Folia Scient. Univ. Tech. Resoviensis, Mat. 19 (1996), 101–105. [24] H.M. Srivastava, Operators of basic (or q-)calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A Sci. 44 (2020), no. 1, 327–344. | ||
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