Certain subclass of strongly meromorphic close to convex functions
Main Article Content
Abstract
The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
References
[1] V. V. Anh and P. D. Tuan, On β-convexity of certain starlike functions, Rev. Roum. Math. Pures et Appl. Vol. 25, 1413–1424, 1979. Google Scholar
[2] M. K. Aouf, On a class of p-valent starlike functions of order α, Int. J. Math. Math. Sci. 10 (4) (1987), 733–744. https://doi.org/10.1155/S0161171287000838 Google Scholar
[3] J. Clunie, On meromorphic schlicht functions, J. Lond. Math. Soc. 34 (1959), 215–216. https://doi.org/10.1112/jlms/s1-34.2.215 Google Scholar
[4] C.Y. Gao, S.Q. Zhou, On a class of analytic functions related to the starlike functions, Kyungpook Math. J. 45 (2005), 123–130. https://koreascience.kr/article/JAKO200510102455991.pdf Google Scholar
[5] G. M. Goluzin, Some estimates for coefficients of univalent functions, Matematicheskii Sbornik 3 (45) (1938), 321–330. Google Scholar
[6] W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Pol. Math. 28 (1973), 297–326. https://doi.org/10.4064/AP-28-3-297-326 Google Scholar
[7] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185. https://doi.org/10.1307/MMJ/1028988895 Google Scholar
[8] J. Kowalczyk and E. Les-Bomba, On a subclass of close-to-convex functions, Appl. Math. Letters 23 (2010), 1147–1151. https://doi.org/10.1016/j.aml.2010.03.004 Google Scholar
[9] S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Vol. 225, Marcel Dekker, New York, USA, 2000. https://doi.org/10.1201/9781482289817 Google Scholar
[10] Y. Polatoglu, M. Bolkal, A. Sen and E. Yavuz, A study on the generalization of Janowski function in the unit disc, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 22 (2006), 27–31. https://real.mtak.hu/186869/1/amapn22_04.pdf Google Scholar
[11] C. Pommerenke, On meromorphic starlike functions, Pacific J. Math. 13 (1963), 221–235. https://doi.org/10.2140/PJM.1963.13.221 Google Scholar
[12] J. K. Prajapat, A new subclass of close-to-convex functions, Surveys in Math. and its Appl. 11 (2016), 11–19. https://www.utgjiu.ro/math/sma/v11/p11_02.pdf Google Scholar
[13] R. K. Raina, P. Sharma and J. Sokol, A class of strongly close-to-convex functions, Bol. Soc. Paran. Mat. 38 (6) (2020), 9–24. https://doi.org/10.5269/bspm.v38i6.38464 Google Scholar
[14] W. Rogosinski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc. 48 (2) (1943), 48–825. https://doi.org/10.1112/plms/s2-48.1.48 Google Scholar
[15] Y. J. Sim and O. S. Kown, A subclass of meromorphic close-to-convex functions of Janowski’s type, Int. J. Math. Math. Sci. Vol. 2012, Article Id. 682162, 12 pages. https://doi.org/10.1155/2012/682162 Google Scholar
[16] A. Soni and S. Kant, A new subclass of meromorphic close-to-convex functions, J. Complex Anal. Vol. 2013, Article Id. 629394, 5 pages. https://doi.org/10.1155/2013/629394 Google Scholar
[17] Z. G. Wang, Y. Sun and N. Xu, Some properties of certain meromorphic close-to-convex functions, Appl. Math. Letters 25 (3) (2012), 454–460. https://doi.org/10.1016/j.aml.2011.09.035 Google Scholar