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Keywords:
analytic function; starlike function; convex function; Hadamard product; Miller-Ross-type Poisson distribution series
analytic function; starlike function; convex function; Hadamard product; Miller-Ross-type Poisson distribution series
Summary:
The purpose of the present paper is to find a necessary and sufficient condition for the Miller-Ross-type Poisson distribution series to be in the class $\mathcal {P}^{\ast }(\alpha ,\beta ,\gamma )$ of analytic functions with negative coefficients. Also, we investigate several inclusion properties of the classes of Janowski type close-to-starlike functions, Janowski type close-to-convex functions and Janowski type quasi-convex functions associated with the operator $\mathbb {I}_{\theta ,\epsilon }^{s}$ defined by this distribution. Further, we consider an integral operator related to the Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered.
References:
[1] Ahmad, M., Frasin, B., Murugusundaramoorthy, G., Al-Khazaleh, A.: An application of Mittag-Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains. Heliyon 7 (2021), Article ID e08109, 5 pages. DOI 10.1016/j.heliyon.2021.e08109
[2] Al-Hawary, T., Frasin, B. A., Yousef, F.: Coefficient estimates for certain classes of analytic functions of complex order. Afr. Mat. 29 (2018), 1265-1271. DOI 10.1007/s13370-018-0623-z | MR 3869566 | Zbl 1413.30029
[3] ntaş, O. Altı: On the coefficients of certain analytic functions. Math. Jap. 33 (1988), 653-659. MR 0972373 | Zbl 0653.30006
[4] ntaş, O. Altı, Irmak, H., Owa, S., Srivastava, H. M.: Coefficient bounds for some families of starlike and convex functions of complex order. Appl. Math. Lett. 20 (2007), 1218-1222. DOI 10.1016/j.aml.2007.01.003 | MR 2384250 | Zbl 1139.30005
[5] ntaş, O. Altı, Kiliç, Ã.Ã.: Coefficient estimates for a class containing quasi-convex functions. Turk. J. Math. 42 (2018), 2819-2825. DOI 10.3906/mat-1805-90 | MR 3866193 | Zbl 1424.30025
[6] Amourah, A., Frasin, B. A., Ahmad, M., Yousef, F.: Exploiting the Pascal distribution series and Gegenbauer polynomials to construct and study a new subclass of analytic bi-univalent functions. Symmetry 14 (2022), Article ID 147, 8 pages. DOI 10.3390/sym14010147
[7] Attiya, A. A.: Some applications of Mittag-Leffler function in the unit disk. Filomat 30 (2016), 2075-2081. DOI 10.2298/FIL1607075A | MR 3535604 | Zbl 1458.30006
[8] Bansal, D., Prajapat, J. K.: Certain geometric properties of the Mittag-Leffler functions. Complex Var. Elliptic Equ. 61 (2016), 338-350. DOI 10.1080/17476933.2015.1079628 | MR 3454110 | Zbl 1336.33039
[9] Cho, N. E., Woo, S. Y., Owa, S.: Uniform convexity properties for hypergeometric functions. Fract. Calc. Appl. Anal. 5 (2002), 303-313. MR 1922272 | Zbl 1028.30013
[10] El-Ashwah, R. M., Kota, W. Y.: Some condition on a Poisson distribution series to be in subclasses of univalent functions. Acta Univ. Apulensis, Math. Inform. 51 (2017), 89-103. DOI 10.17114/j.aua.2017.51.08 | MR 3711116 | Zbl 1413.30053
[11] El-Deeb, S. M., Bulboacă, T., Dziok, J.: Pascal distribution series connected with certain subclasses of univalent functions. Kyungpook Math. J. 59 (2019), 301-314. DOI 10.5666/KMJ.2019.59.2.301 | MR 3987710 | Zbl 1435.30045
[12] Frasin, B. A., Al-Hawary, T., Yousef, F.: Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions. Afr. Mat. 30 (2019), 223-230. DOI 10.1007/s13370-018-0638-5 | MR 3927324 | Zbl 1438.30042
[13] Frasin, B. A., Al-Hawary, T., Yousef, F.: Some properties of a linear operator involving generalized Mittag-Leffler function. Stud. Univ. Babeş-Bolyai, Math. 65 (2020), 67-75. DOI 10.24193/subbmath.2020.1.06 | MR 4085426 | Zbl 1513.33050
[14] Frasin, B. A., Aydoğan, S. M.: Pascal distribution series for subclasses of analytic functions associated with conic domains. Afr. Mat. 32 (2021), 105-113. DOI 10.1007/s13370-020-00813-1 | MR 4222458 | Zbl 1474.30075
[15] Frasin, B. A., Gharaibeh, M. M.: Subclass of analytic functions associated with Poisson distribution series. Afr. Mat. 31 (2020), 1167-1173. DOI 10.1007/s13370-020-00788-z | MR 4154545 | Zbl 1463.30053
[16] Frasin, B. A., Murugusundaramoorthy, G., Aouf, M. K.: Subclasses of analytic functions associated with Mittag-Leffler-type Poisson distribution. Palest. J. Math. 11 (2022), 496-503. MR 4345785 | Zbl 1494.30025
[17] Garg, M., Manohar, P., Kalla, S. L.: A Mittag-Leffler-type function of two variables. Integral Transforms Spec. Funct. 24 (2013), 934-944. DOI 10.1080/10652469.2013.789872 | MR 3172007 | Zbl 1292.33020
[18] Gupta, V. P., Jain, P. K.: Certain classes of univalent functions with negative coefficients. II. Bull. Aust. Math. Soc. 15 (1976), 467-473. DOI 10.1017/S0004972700022917 | MR 0435374 | Zbl 0335.30010
[19] Janowski, W.: Some extremal problems for certain families of analytic functions. I. Ann. Pol. Math. 28 (1973), 297-326. DOI 10.4064/ap-28-3-297-326 | MR 0328059 | Zbl 0275.30009
[20] Joshi, S. B., Joshi, S. S., Pawar, H. H., Ritelli, D.: Connections between normalized Wright functions with families of analytic functions with negative coefficients. Analysis, München 42 (2022), 111-119. DOI 10.1515/anly-2021-1027 | MR 4415955 | Zbl 1510.33018
[21] Kaplan, W.: Close-to-convex schlicht functions. Mich. Math. J. 1 (1952), 169-185. DOI 10.1307/mmj/1028988895 | MR 0054711 | Zbl 0048.31101
[22] Kim, H. S., Lee, S. K.: Some classes of univalent functions. Math. Jap. 32 (1987), 781-796. MR 0918290 | Zbl 0648.30010
[23] Kulkarni, S. R.: Some Problems Connected with Univalent Functions: Ph.D. Thesis. Shivaji University, Kolhapur (1981).
[24] Merkes, E. P., Scott, W. T.: Starlike hypergeometric functions. Proc. Am. Math. Soc. 12 (1961), 885-888. DOI 10.1090/S0002-9939-1961-0143950-1 | MR 143950 | Zbl 0102.06502
[25] Miller, K. S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, New York (1993). MR 1219954 | Zbl 0789.26002
[26] Mittag-Leffler, G.: Sur la nouvelle fonction $E_{\alpha}(x)$. C. R. Acad. Sci. Paris 137 (1904), 554-558 French \99999JFM99999 34.0435.01.
[27] Murugusundaramoorthy, G., Frasin, B. A., Al-Hawary, T.: Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series. Math. Bohem. 147 (2022), 407-417. DOI 10.21136/MB.2021.0132-20 | MR 4482314 | Zbl 1524.30070
[28] Murugusundaramoorthy, G., Vijaya, K., Porwal, S.: Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series. Hacet. J. Math. Stat. 45 (2016), 1101-1107. DOI 10.15672/HJMS.20164513110 | MR 3585439 | Zbl 1359.30022
[29] Noor, K. I., Thomas, D. K.: Quasi-convex univalent functions. Int. J. Math. Math. Sci. 3 (1980), 255-266. DOI 10.1155/S016117128000018X
[30] Porwal, S.: An application of a Poisson distribution series on certain analytic functions. J. Complex Anal. 2014 (2014), Article ID 984135, 3 pages. DOI 10.1155/2014/984135 | MR 3173344 | Zbl 1310.30017
[31] Reade, M. O.: On close-to-convex univalent functions. Mich. Math. J. 3 (1955), 59-62. DOI 10.1307/mmj/1031710535 | MR 0070715 | Zbl 0070.07302
[32] Şeker, B., Eker, S. S., Çekiç, B.: On subclass of analytic functions associated with MillerRoss-type Poisson distribution series. Sahand Commun. Math. Anal. 19 (2022), 69-79. DOI 10.22130/scma.2022.551474.1091 | Zbl 1513.30085
[33] Shamaki, A., Frasin, B. A., Seoudy, T. M.: Subclass of analytic functions related with Pascal distribution series. J. Math. 2022 (2022), Article ID 8355285, 5 pages. DOI 10.1155/2022/8355285 | MR 4392098
[34] Silverman, H.: Starlike and convexity properties for hypergeometric functions. J. Math. Anal. Appl. 172 (1993), 574-581. DOI 10.1006/jmaa.1993.1044 | MR 1201006 | Zbl 0774.30015
[35] Silverman, H., Silvia, E. M.: Subclasses of starlike functions subordinate to convex functions. Can. J. Math. 37 (1985), 48-61. DOI 10.4153/CJM-1985-004-7 | MR 0777038 | Zbl 0574.30015
[36] Themangani, R., Porwal, S., Magesh, N.: Generalized hypergeometric distribution and its applications on univalent functions. J. Inequal. Appl. 2020 (2020), Article ID 249, 10 pages. DOI 10.1186/s13660-020-02515-5 | MR 4179869 | Zbl 1503.30047
[37] Wiman, A.: Über die Nullstellen der Funktionen $E_{\alpha}(x)$. Acta Math. 29 (1905), 217-134 German \99999JFM99999 36.0472.01. DOI 10.1007/BF02403204 | MR 1555016
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