Title:
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Properties on subclass of Sakaguchi type functions using a Mittag-Leffler type Poisson distribution series (English) |
Author:
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Nithiyanandham, Elumalai Krishnan |
Author:
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Keerthi, Bhaskara Srutha |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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149 |
Issue:
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4 |
Year:
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2024 |
Pages:
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455-470 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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}\text {-}\nobreak \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. (English) |
Keyword:
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Mittag-Leffler type Poisson distribution |
Keyword:
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analytic function |
Keyword:
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conic-type region |
Keyword:
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geometric properties |
MSC:
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30C45 |
MSC:
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30C50 |
DOI:
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10.21136/MB.2023.0061-23 |
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Date available:
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2024-12-13T19:03:35Z |
Last updated:
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2024-12-13 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/152673 |
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Reference:
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[1] Agarwal, R. P.: A propos d'une note de M. Pierre Humbert.C. R. Acad. Sci., Paris 236 (1953), 2031-2032 French. Zbl 0051.30801, MR 0055502 |
Reference:
|
[2] Alessa, N., Venkateswarlu, B., Reddy, P. T., Loganathan, K., Tamilvanan, K.: A new subclass of analytic functions related to Mittag-Leffler type Poisson distribution series.J. Funct. Spaces 2021 (2021), Article ID 6618163, 7 pages. Zbl 1461.30036, MR 4214806, 10.1155/2021/6618163 |
Reference:
|
[3] Kanas, S., Răducanu, D.: Some class of analytic functions related to conic domains.Math. Slovaca 64 (2014), 1183-1196. Zbl 1349.30054, MR 3277846, 10.2478/s12175-014-0268-9 |
Reference:
|
[4] Kanas, S., Srivastava, H. M.: Linear operators associated with $k$-uniformly convex functions.Integral Transforms Spec. Funct. 9 (2000), 121-132. Zbl 0959.30007, MR 1784495, 10.1080/10652460008819249 |
Reference:
|
[5] Kanas, S., Wiśniowska, A.: Conic regions and $k$-uniform convexity.J. Comput. Appl. Math. 105 (1999), 327-336. Zbl 0944.30008, MR 1690599, 10.1016/S0377-0427(99)00018-7 |
Reference:
|
[6] Kanas, S., Wiśniowska, A.: Conic domains and starlike functions.Rev. Roum. Math. Pures Appl. 45 (2000), 647-657. Zbl 0990.30010, MR 1836295 |
Reference:
|
[7] Khan, M. G., Ahmad, B., Khan, N., Mashwani, W. K., Arjika, S., Khan, B., Chinram, R.: 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. Zbl 1508.30027, MR 4296642, 10.1155/2021/4343163 |
Reference:
|
[8] Mahmood, T., Naeem, M., Hussain, S., Khan, S., Altinkaya, Ş.: A subclass of analytic functions defined by using Mittag-Leffler function.Honam Math. J. 42 (2020), 577-590. Zbl 1467.30010, MR 4161224, 10.5831/HMJ.2020.42.3.577 |
Reference:
|
[9] Mittag-Leffler, G. M.: Une généralisation de l'intégrale de Laplace-Abel.C. R. Acad. Sci., Paris 136 (1903), 537-539 French \99999JFM99999 34.0434.02. |
Reference:
|
[10] Mittag-Leffler, G. M.: Sur la nouvelle fonction $E_{\alpha}(x)$.C. R. Acad. Sci., Paris 137 (1904), 554-558 French \99999JFM99999 34.0435.01. |
Reference:
|
[11] Mittag-Leffler, G.: Sur la représentation analytique d'une branche uniforme d'une fonction monogène.Acta Math. 29 (1905), 101-181 French \99999JFM99999 36.0469.02. MR 1555012, 10.1007/BF02403200 |
Reference:
|
[12] Noor, K. I., Malik, S. N.: On coefficient inequalities of functions associated with conic domains.Comput. Math. Appl. 62 (2011), 2209-2217. Zbl 1231.30011, MR 2831681, 10.1016/j.camwa.2011.07.006 |
Reference:
|
[13] Porwal, S., Dixit, K. K.: On Mittag-Leffler type Poisson distribution.Afr. Mat. 28 (2017), 29-34. Zbl 1373.60033, MR 3613617, 10.1007/s13370-016-0427-y |
Reference:
|
[14] Wiman, A.: Über den Fundamentalsatz in der Theorie der Funktionen $E_\alpha(x)$.Acta Math. 29 (1905), 191-201 German \99999JFM99999 36.0471.01. MR 1555014, 10.1007/BF02403202 |
Reference:
|
[15] Wiman, A.: Über die Nullstellen der Funktionen $E_\alpha(x)$.Acta Math. 29 (1905), 217-234 German \99999JFM99999 36.0472.01. MR 1555016, 10.1007/BF02403204 |
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