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

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

Two new subclasses Qp,k(λ,A,B) and Gp,k(λ,A,B) of analytic and pvalent 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.

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  • 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 -starlike and -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 -convex and -quasiconvex functions with respect to n-symmetric points , Appl. Math. Comput. 188, 1142-1150, 2007.