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

Year 2018, Volume: 47 Issue: 5, 1156 - 1171, 16.10.2018

Abstract

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.

References

  • 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.
Year 2018, Volume: 47 Issue: 5, 1156 - 1171, 16.10.2018

Abstract

References

  • 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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yi-hui Xu This is me

Jin-lin Liu

Publication Date October 16, 2018
Published in Issue Year 2018 Volume: 47 Issue: 5

Cite

APA Xu, Y.-h., & Liu, J.-l. (2018). On certain multivalent analytic functions starlike with respect to $k$-symmetric points. Hacettepe Journal of Mathematics and Statistics, 47(5), 1156-1171.
AMA Xu Yh, Liu Jl. On certain multivalent analytic functions starlike with respect to $k$-symmetric points. Hacettepe Journal of Mathematics and Statistics. October 2018;47(5):1156-1171.
Chicago Xu, Yi-hui, and Jin-lin Liu. “On Certain Multivalent Analytic Functions Starlike With Respect to $k$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics 47, no. 5 (October 2018): 1156-71.
EndNote Xu Y-h, Liu J-l (October 1, 2018) On certain multivalent analytic functions starlike with respect to $k$-symmetric points. Hacettepe Journal of Mathematics and Statistics 47 5 1156–1171.
IEEE Y.-h. Xu and J.-l. Liu, “On certain multivalent analytic functions starlike with respect to $k$-symmetric points”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, pp. 1156–1171, 2018.
ISNAD Xu, Yi-hui - Liu, Jin-lin. “On Certain Multivalent Analytic Functions Starlike With Respect to $k$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics 47/5 (October 2018), 1156-1171.
JAMA Xu Y-h, Liu J-l. On certain multivalent analytic functions starlike with respect to $k$-symmetric points. Hacettepe Journal of Mathematics and Statistics. 2018;47:1156–1171.
MLA Xu, Yi-hui and Jin-lin Liu. “On Certain Multivalent Analytic Functions Starlike With Respect to $k$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 5, 2018, pp. 1156-71.
Vancouver Xu Y-h, Liu J-l. On certain multivalent analytic functions starlike with respect to $k$-symmetric points. Hacettepe Journal of Mathematics and Statistics. 2018;47(5):1156-71.