On certain multivalent analytic functions starlike with respect to $k$-symmetric points

Yıl 2018, Cilt: 47 Sayı: 5, 1156 - 1171, 16.10.2018

Yi-hui Xu Jin-lin Liu

Öz

Two new subclasses $Q_{p,k}(\lambda, A,B)$ and $G_{p,k}(\lambda, A,B)$ of analytic and $p$-valent functions which are starlike with respect to $k$-symmetric points are introduced. Distortion bounds, inclusion relations, integral transforms and convolution properties for these classes are studied.

Anahtar Kelimeler

Analytic function, convolution, subordination, distortion bound, inclusion relation, integral transform, symmetric point

Kaynakça

• Aouf, M.K., Dziok, J. and Sokol, J. On a subclass of strongly starlike functions, Appl. Math. Lett. 24, 27-32, 2011.
• Cho, N.E., Kwon, O.S. and Owa, S. Certain subclasses of Sakaguchi functions, Southeast Asian Bull. Math. 17, 121-126, 1993.
• Dziok, J. and Sokol, J. Some inclusion properties of certain class of analytic functions, Taiwanese J. Math. 13, 2001-2009, 2009.
• Dziok, J., Raina, R.K. and Sokol, J. On alpha-convex functions related to shell-like functions connected with Fibonacci numbers, Appl. Math. Comput. 218, 966-1002, 2011.
• Halim, S.A. Functions starlike with respect to other points, Int. J. Math. Math. Sci. 14, 451-456, 1991.
• Pavatham, R. and Radha, S. On $\alpha$-starlike and $\alpha$-close-to-convex functions with respect to $n$-symmetric points, Indina J. Pure Appl. Math. 16, 1114-1122, 1986.
• Sakaguchi, K. On a certain univalent mapping, J. Math. Soc.Japan 11, 72-75, 1959.
• Sokol, J. A certain class of starlike functions, Comput. Math. Appl. 62, 611-619, 2011.
• Srivastava, H.M., Yang, D.-G. and Xu, N-E. Some subclasses of meromorphically multivalent functions associated with a linear operator, Appl. Math. Comput. 195, 11-23, 2008.
• Stantiewics, J. Some remarks on functions starlike with respect to symmetric points, Ann. Univ. Mariae Curie-Sklodowska 19, 53-59, 1965.
• Wang, Z.-G., Gao, C.-Y. and Yuan, S.-M. On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322, 97- 106, 2006.
• Wu, Z. On classes of Sakaguchi functions and Hadamard products, Sci. Sinica Ser. A30, 128-135, 1987.
• Xu, N-E. and Yang, D.-G. Some classes of analytic and multivalent functions involving a linear operator, Math. Comput. Modelling 49, 955-965, 2009.
• Yuan, S.-M. and Liu, Z.-M. Some properties of $\alpha$-convex and $\alpha$-quasiconvex functions with respect to $n$-symmetric points, Appl. Math. Comput. 188, 1142-1150, 2007.