Previous |  Up |  Next

Article

Keywords:
uniformly starlike function; uniformly convex function; starlike function; convex function; Pascal distribution; convolution
Summary:
In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk $\mathbb {U}$. We also state corollaries of our main results.
References:
[1] nkaya, Ş. Altı, n, S. Yalçı: Poisson distribution series for certain subclasses of starlike functions with negative coefficients. An. Univ. Oradea, Fasc. Mat. 24 (2017), 5-8. MR 3931277 | Zbl 1399.30027
[2] nkaya, Ş. Altı, n, S. Yalçı: Poisson distribution series for analytic univalent functions. Complex Anal. Oper. Theory 12 (2018), 1315-1319. DOI 10.1007/s11785-018-0764-y | MR 3800974 | Zbl 1393.30012
[3] Çakmak, S., n, S. Yalçı, nkaya, Ş. Altı: Some connections between various classes of analytic functions associated with the power series distribution. Sakarya Univ. J. Sci. 23 (2019), 982-985.
[4] 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
[5] Branges, L. de: A proof of the Bieberbach conjucture. Acta Math. 154 (1985), 137-152. DOI 10.1007/BF02392821 | MR 0772434 | Zbl 0573.30014
[6] 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 07167097
[7] 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 0143950 | Zbl 0102.06502
[8] Murugusundaramoorthy, G.: Subclasses of starlike and convex functions involving Poisson distribution series. Afr. Mat. 28 (2017), 1357-1366. DOI 10.1007/s13370-017-0520-x | MR 3714601 | Zbl 1381.30015
[9] 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
[10] Owa, S., Srivastava, H. M.: Univalent and starlike generalized hypergeometric functions. Can. J. Math. 39 (1987), 1057-1077. DOI 10.4153/CJM-1987-054-3 | MR 0918587 | Zbl 0611.33007
[11] Porwal, S.: Mapping properties of generalized Bessel functions on some subclasses of univalent functions. An. Univ. Oradea, Fasc. Mat. 20 (2013), 51-60. MR 3154762 | Zbl 1313.30070
[12] 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
[13] Porwal, S., nkaya, Ş. Altı, n, S. Yalçı: The Poisson distribution series of general sublasses of univalent functions. Acta Univ. Apulensis, Math. Inform. 58 (2019), 45-52. DOI 10.17114/j.aua.2019.58.04 | MR 3973322 | Zbl 07122534
[14] Porwal, S., Kumar, M.: A unified study on starlike and convex functions associated with Poisson distribution series. Afr. Mat. 27 (2016), 1021-1027. DOI 10.1007/s13370-016-0398-z | MR 3536083 | Zbl 1352.30014
[15] Rosy, T., Stephen, B. A., Subramanian, K. G., Silverman, H.: Classes of convex functions. Int. J. Math. Math. Sci. 23 (2000), 819-825. DOI 10.1155/S0161171200003082 | MR 1769866 | Zbl 0957.30009
[16] 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
[17] Srivastava, H. M., Murugusundaramoorthy, G., Sivasubramanian, S.: Hypergeometric functions in the parabolic starlike and uniformly convex domains. Integral Transforms Spec. Funct. 18 (2007), 511-520. DOI 10.1080/10652460701391324 | MR 2348596 | Zbl 1198.30013
[18] Subramanian, K. G., Murugusundaramoorthy, G., Balasubrahmanyam, P., Silverman, H.: Subclasses of uniformly convex and uniformly starlike functions. Math. Jap. 42 (1995), 517-522. MR 1363841 | Zbl 0837.30011
Partner of
EuDML logo