Some applications of a Wright distribution series on subclasses of univalent functions
DOI:
https://doi.org/10.24193/subbmath.2024.4.04Keywords:
analytic functions, starlike function, convex function, probability distribution, Wright distribution seriesAbstract
The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with wright distribution to be in subclasses of univalent functions and inclusion relations for such subclasses in the open unit disk. Further, we consider the properties of integral operator related to Wright distribution series.References
Altınkaya, S¸. Yal¸cın, S., Poisson distribution series for analytic univalent functions, Complex Anal. Oper. Theory, 12, (2019), no. 5, 1315-1319.
https://doi.org/10.1007/s11785-018-0764-y
Arif, M., Umar, S., Mahmood, S., New reciprocal class of analytic functions associated with linear operator. Iran. J. Sci. Technol. Trans. Sci., 42, (2018), 881-886. https://doi.org/10.1007/s40995-016-0059-y
Al-Hawar, T., Frasin, B. A., Coefficient estimates and subordination properties for certain classes of analytic functions of reciprocal order, Stud. Univ. Babes Bolyai Math., 63, (2018), no. 2, 203-212.
Dixit, K. K., Pal, S. K., On a class of univalent functions related to complex order, Indian J. Pure Appl. Math., 26, (1995), no. 9, 889–896.
El-Deeb, S. M., Bulboac˘a, T., Dziok, J., Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Math. J., 59, (2019), no. 2, 301-314.
Eker, S. S., Murugusundaramoorthy, G., S¸eker, B. Spiral-like functions associated with Miller–Ross-type Poisson distribution series, Bol. Soc. Mat. Mex. 29, 16 (2023). https://doi.org/10.1007/s40590-022-00488-7
Frasin, B. A., Talafha, Y., Al-Hawary, T., Subordination results for classes of functions of reciprocal order, Tamsui Oxford J. Info. Math. Sci., 30, (2014), 81-89.
Frasin, B. A., Abd Sabri, M., Sufficient conditions for starlikeness of reciprocal order, Eur. J. Pure Appl. Math., 10, (2017), no. 4, 871-876.
Gorenflo, R., Luchko, Y., Mainardi, F., Analytic properties and applications of Wright functions, Fract. Calc. Appl. Anal., 2, (1999), no. 4, 383-414.
Murugusundaramoorthy, G., Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat., 28, (2017), 1357-1366. https://doi.org/10.1007/s13370-017-0520-x
Kamali, M., Riskulova, A., On subordination results for certain classes of analytic functions of reciprocal order, Int. J. Anal. Appl., 19, (2021), no. 1, 123-137. https://doi.org/10.28924/2291-8639-19-2021-123
Kumar, V., Kumar S., Cho, N. E., Certain Coefficient functionals for Starlike functions of reciprocal order alpha, Thai J. Math., 20, (2022), no. 3, 1183-1197.
Maharana, S., Sahoo, S. K., Inclusion properties of planar harmonic mappings associated with the Wright function, Complex Variables and Elliptic Equations, 66, (2021), no. 10, 1619-1641. https://doi.org/10.1080/17476933.2020.1772765
Maharana, S., Prajapat, J. K., Bansal, D., Geometric properties of Wright function, Math. Bohem., 143, (2018), no. 1, 99–111.
https://doi.org/10.21136/MB.2017.0077-16
Mustafa, N., Geometric properties of normalized Wright function, Math. Comput. Appl., 21, no. 14, (2016). https://doi.org/10.3390/mca21020014
Mustafa, N., Nezir, V., Dutta, H., Geometric Properties of Normalized Wright Functions. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. (2020). https://doi.org/10.1007/978-3-319-99918-0-22
Mahmood, S., Sokol, J., Srivastava, H. M., Malik, S. N., Some reciprocal classes of close-to-convex and quasi-convex analytic functions, Mathematics, 7, (2019), no. 4, 309. https://doi.org/10.3390/math7040309
Nazeer, W., Mehmood, Q., Kang, S. M., Haq, A. U., An application of Binomial distribution series on certain analytic functions, J. Comput. Anal. Appl., 26, (2019), 11-17.
Noor, K. I., Khan, N., Ahmad, Q. Z., Coefficient bounds for a subclass of multivalent functions of reciprocal order, Mathematics, 2, (2017), no. 2, 322- 335. https://doi.org/ 10.3934/Math.2017.2.322
Nunokawa, M., Owa, S., Nishiwaki, J., Kuroki, K., Hayami, T., Differential subordination and argumental property, Comput. Math. Appl., 56, (2008), no. 10, 2733-2736. https://doi.org/10.1016/j.camwa.2008.02.050
Owa, S., Srivastava, H. M., Some generalized convolution properties associated with certain subclasses of analytic functions, J. Ineq. Pure Appl. Math, 3, (2002), 1-13.
Prajapat, J. K., Certain geometric properties of the Wright
function, Integral Transforms Spec. Funct., 26, (2015), 203-212.
https://doi.org/10.1080/10652469.2014.983502
Porwal, S., Ahamad, D., An application of hypergeometric distribution type series on certain analytic functions, Thai J. Math., 18, (2019), no. 4, 2071- 2078.
Porwal, S., Pathak, A. L., Mishra, O., Wright distribution and its applications on univalent functions, U.P.B. Sci. Bull., Series A, 84, (2022), no. 4, 81-88.
Porwal, S., Kumar, M., A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27, (2016), no. 5, 1021–1027.
https://doi.org/10.1007/s13370-016-0398-z
Polatoglu, Y., Blocal, M., Sen, A., Yavuz, E., An investigation on a subclass of p-valently starlike functions in the unit disc, Turk. J. Math., 31, (2007), 221-228.
Robertson, M. S., Univalent functions f(z) for which zf ’(z) is spirallike, Michigan Math. J., 16, (1969), 315-324.
Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51, (1975), 109-116.
Ravichandran, V., Sivaprasad Kumar, S., Argument estimate for starlike functions of reciprocal order, Southeast Asian Bull. Math., 35, (2011), no. 5, 837-843.
Shrigan, M. G., Yal¸cin, S., Altınkaya, S¸., Unified approach to starlike and convex functions involving Poisson distribution series, Bul. Acad. S¸tiint¸e Repub. Moldova Mat., 97, (2021), no. 3, 11-20.
Uyanik, N., Shiraishi, H., Owa, S., Polatoglu, Y., Reciprocal classes of p-valently spirallike and p-valently Robertson functions, J. Ineq. Appl., (2011), 1-10. https://doi.org/10.1186/1029-242X-2011-61
Venkateswarlu, B. Vamshee Krishna, D., Rani, N., Third Hankel determinant for the inverse of reciprocal of bounded turning functions, Bul. acad. stiinte Repub. Moldova Mat., 79, (2015), no. 3, 50-59.
Wright, E. M., On the coefficients of power series having exponential Singularities, J. London Math. Soc., 8 (1993), 71-79.
Wanas, A. K., Khuttar, J. A., Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci., 4, (2020), no. 1, 71-82.