Received April 6, 2023. Published online November 21, 2023.
Abstract: Few subclasses of Sakaguchi type functions are introduced in this article, based on the notion of Mittag-Leffler type Poisson distribution series. The class $ \mathfrak{p}-\Phi\mathcal{S}^*(t,\mu,\nu,J,K) $ is defined, and the necessary and sufficient condition, convex combination, growth distortion bounds, and partial sums are discussed.
References: [1] R. P. Agarwal: A propos d'une note de M. Pierre Humbert. C. R. Acad. Sci., Paris 236 (1953), 2031-2032. (In French.) MR 0055502 | Zbl 0051.30801
[2] N. Alessa, B. Venkateswarlu, P. T. Reddy, K. Loganathan, K. Tamilvanan: A new subclass of analytic functions related to Mittag-Leffler type Poisson distribution series. J. Funct. Spaces 2021 (2021), Article ID 6618163, 7 pages. DOI 10.1155/2021/6618163 | MR 4214806 | Zbl 1461.30036
[3] S. Kanas, D. Răducanu: Some class of analytic functions related to conic domains. Math. Slovaca 64 (2014), 1183-1196. DOI 10.2478/s12175-014-0268-9 | MR 3277846 | Zbl 1349.30054
[4] S. Kanas, H. M. Srivastava: Linear operators associated with $k$-uniformly convex functions. Integral Transforms Spec. Funct. 9 (2000), 121-132. DOI 10.1080/10652460008819249 | MR 1784495 | Zbl 0959.30007
[5] S. Kanas, A. Wiśniowska: Conic regions and $k$-uniform convexity. J. Comput. Appl. Math. 105 (1999), 327-336. DOI 10.1016/S0377-0427(99)00018-7 | MR 1690599 | Zbl 0944.30008
[6] S. Kanas, A. Wiśniowska: Conic domains and starlike functions. Rev. Roum. Math. Pures Appl. 45 (2000), 647-657. MR 1836295 | Zbl 0990.30010
[7] M. G. Khan, B. Ahmad, N. Khan, W. K. Mashwani, S. Arjika, B. Khan, R. Chinram: Applications of Mittag-Leffler type Poisson distribution to a subclass of analytic functions involving conic-type regions. J. Funct. Spaces 2021 (2021), Article ID 4343163, 9 pages. DOI 10.1155/2021/4343163 | MR 4296642 | Zbl 1508.30027
[8] T. Mahmood, M. Naeem, S. Hussain, S. Khan, Ş. Altinkaya: A subclass of analytic functions defined by using Mittag-Leffler function. Honam Math. J. 42 (2020), 577-590. DOI 10.5831/HMJ.2020.42.3.577 | MR 4161224 | Zbl 1467.30010
[9] G. M. Mittag-Leffler: Une généralisation de l'intégrale de Laplace-Abel. C. R. Acad. Sci., Paris 136 (1903), 537-539. (In French.) JFM 34.0434.02
[10] G. M. Mittag-Leffler: Sur la nouvelle fonction $E_{\alpha}(x)$. C. R. Acad. Sci., Paris 137 (1904), 554-558. (In French.) JFM 34.0435.01
[11] G. Mittag-Leffler: Sur la représentation analytique d'une branche uniforme d'une fonction monogène. Acta Math. 29 (1905), 101-181. (In French.) DOI 10.1007/BF02403200 | MR 1555012 | JFM 36.0469.02
[12] K. I. Noor, S. N. Malik: On coefficient inequalities of functions associated with conic domains. Comput. Math. Appl. 62 (2011), 2209-2217. DOI 10.1016/j.camwa.2011.07.006 | MR 2831681 | Zbl 1231.30011
[13] S. Porwal, K. K. Dixit: On Mittag-Leffler type Poisson distribution. Afr. Mat. 28 (2017), 29-34. DOI 10.1007/s13370-016-0427-y | MR 3613617 | Zbl 1373.60033
[14] A. Wiman: Über den Fundamentalsatz in der Theorie der Funktionen $E_\alpha(x)$. Acta Math. 29 (1905), 191-201. (In German.) DOI 10.1007/BF02403202 | MR 1555014 | JFM 36.0471.01
[15] A. Wiman: Über die Nullstellen der Funktionen $E_\alpha(x)$. Acta Math. 29 (1905), 217-234. (In German.) DOI 10.1007/BF02403204 | MR 1555016 | JFM 36.0472.01
Affiliations: Elumalai Krishnan Nithiyanandham, Bhaskara Srutha Keerthi (corresponding author), Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Chennai Campus, Chennai-600 127, India, e-mail: nithiyankrish@gmail.com, keerthivitmaths@gmail.com
