Year 2021,
Volume: 70 Issue: 2, 849 - 857, 31.12.2021
Bilal Şeker
,
Sevtap Sümer Eker
References
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- Altintaş, O., Özkan, Ö., Srivastava, H. M., Neighorhoods of a class of analytic functions with negative coefficient, Applied Mathematics Letters, 13(3) (2000), 63-67. https://doi.org/10.1016/S0893-9659(99)00187-1
- Çakmak, S., Yalçın, S., Altınkaya, ¸S., Some connections between various classes of analytic functions associated with the power series distribution, Sakarya Üniversitesi Fen Bilimleri
Enstitüsü Dergisi, 23(5) (2019), 982-985. https://doi.org/10.16984/saufenbilder.552957
- El-Deeb, S.M., Bulboaca, T., Dziok, J., Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Mathematical Journal, 59(2) (2019), 301-314.
https://doi.org/10.5666/KMJ.2019.59.2.301
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- 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
- Nazeer, W., Mehmood, Q., Kang, S. M., Haq, A. U., An application of Binomial distribution series on certain analytic functions, Journal of Computational Analysis and Applications, 11 (2019).
- Nasr, M. A., Aouf, M. K., Starlike functions of complex order, Journal of Natural Sciences and Mathematics, 25 (1985), 1-12.
- Owa, S., Notes on starlike, convex, and close-to-convex functions of complex order, in : H. M. Srivastava and S. Owa (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, 199-218, Halsted Press. (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
- Porwal, S., An application of a Poisson distribution series on certain analytic functions, Journal of Complex Analysis, 1-3 (2014), Article ID 984135. http://dx.doi.org/10.1155/2014/984135
- Porwal, S., Kumar, M., A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27 (2016), 1021-1027 https://doi.org/10.1007/s13370-016-0398-z
- Silverman, H., Univalent functions with negative coefficients, Proc. Am.Math. Soc., 51 (1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0
- Wiatrowski, P., The coefficients of a certain family of holomorphic functions, Zeszyty Nauk. Uniw. Lodz Nauk. Mat.-Przyrod, (Ser.II), 39 (1971) 75-85.
On certain subclass of univalent functions of complex order associated with Pascal distribution series
Year 2021,
Volume: 70 Issue: 2, 849 - 857, 31.12.2021
Bilal Şeker
,
Sevtap Sümer Eker
Abstract
In this study, by establishing a connection between normalized univalent functions in the unit disc and Pascal distribution series, we have obtained the necessary and sufficient conditions for these functions to belong to some subclasses of univalent functions of complex-order. We also determined some conditions by considering the integral operator for these functions.
References
- Altınkaya, ¸S., Yalçın, S., Poisson distribution series for analytic univalent functions, Complex Anal. Oper. Theory, 12 (2018), 1315-1319. https://doi.org/10.1007/s11785-018-0764-y
- Altintaş, O., Özkan, Ö., Srivastava, H. M., Neighorhoods of a class of analytic functions with negative coefficient, Applied Mathematics Letters, 13(3) (2000), 63-67. https://doi.org/10.1016/S0893-9659(99)00187-1
- Çakmak, S., Yalçın, S., Altınkaya, ¸S., Some connections between various classes of analytic functions associated with the power series distribution, Sakarya Üniversitesi Fen Bilimleri
Enstitüsü Dergisi, 23(5) (2019), 982-985. https://doi.org/10.16984/saufenbilder.552957
- El-Deeb, S.M., Bulboaca, T., Dziok, J., Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Mathematical Journal, 59(2) (2019), 301-314.
https://doi.org/10.5666/KMJ.2019.59.2.301
- Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften 259, Springer-Verlag, New York, 1983.
- Halim, S. A., On a class of functions of complex order, Tamkang Journal of Mathematics, 30(2) (1999), 147-153. https://doi.org/10.5556/j.tkjm.30.1999.4221
- Murugusundaramoorthy, G., Vijaya, K., Porwal, S., Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacettepe Journal of Mathematics and Statistics, 45(4) (2016), 1101-1107. https://doi.org/10.15672/HJMS.20164513110
- 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
- Nazeer, W., Mehmood, Q., Kang, S. M., Haq, A. U., An application of Binomial distribution series on certain analytic functions, Journal of Computational Analysis and Applications, 11 (2019).
- Nasr, M. A., Aouf, M. K., Starlike functions of complex order, Journal of Natural Sciences and Mathematics, 25 (1985), 1-12.
- Owa, S., Notes on starlike, convex, and close-to-convex functions of complex order, in : H. M. Srivastava and S. Owa (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, 199-218, Halsted Press. (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
- Porwal, S., An application of a Poisson distribution series on certain analytic functions, Journal of Complex Analysis, 1-3 (2014), Article ID 984135. http://dx.doi.org/10.1155/2014/984135
- Porwal, S., Kumar, M., A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27 (2016), 1021-1027 https://doi.org/10.1007/s13370-016-0398-z
- Silverman, H., Univalent functions with negative coefficients, Proc. Am.Math. Soc., 51 (1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0
- Wiatrowski, P., The coefficients of a certain family of holomorphic functions, Zeszyty Nauk. Uniw. Lodz Nauk. Mat.-Przyrod, (Ser.II), 39 (1971) 75-85.