Two new subclasses of p-valent starlike functions

  • Jin-Lin LiuEmail author
  • Rekha Srivastava
Original Paper


In this paper two new subclasses of p-valent starlike functions are introduced and investigated. Inclusion relations, integral transforms, distortion bounds and convolution properties for each of these p-valent function classes are obtained.


Analytic functions p-valent starlike functions Subordination Distortion bounds Inclusion relations Integral transforms Convolution properties 

Mathematics Subject Classification

30C45 30C80 



This work was supported by the National Natural Science Foundation of the Prople’s Republic of China (Grant number 11571299) and the Natural Science Foundation of the Jiangsu Province (Grant number BK20151304).


  1. 1.
    Aouf, M.K., Dziok, J., Sokol, J.: On a subclass of strongly starlike functions. Appl. Math. Lett. 24, 27–32 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cho, N.E., Lee, H.J., Park, J.H., Srivastava, R.: Some applications of the first-order differential subordinations. Filomat 30, 1465–1474 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cho, N.E., Kwon, O.S., Owa, S.: Certain subclasses of Sakaguchi functions. Southeast Asian Bull. Math. 17, 121–126 (1993)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Devi, S., Srivastava, H.M., Swaminathan, A.: Inclusion properties of a class of functions involving the Dziok-Srivastava operator. Korean J. Math. 24, 139–168 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dziok, J.: Classes of meromorphic functions associated with conic regions, Acta Math. Sci. Ser. B Engl. Ed. 32, 765–774 (2012)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Dziok, J.: Classes of multivalent analytic and meromorphic functions with two fixed points. Fixed Point Theory Appl. Article ID 86, 1–18 (2013)Google Scholar
  7. 7.
    Dziok, J., Sokol, J.: Some inclusion properties of certain class of analytic functions. Taiwan. J. Math. 13, 2001–2009 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dziok, J., Raina, R.K., Sokol, J.: On alpha-convex functions related to shell-like functions connected with Fibonacci numbers. Appl. Math. Comput. 218, 966–1002 (2011)zbMATHGoogle Scholar
  9. 9.
    Halim, S.A.: Functions starlike with respect to other points. Int. J. Math. Math. Sci. 14, 451–456 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kwon, O.S., Sim, Y.J., Cho, N.E., Srivastava, H.M.: Some radius problems related to a certain subclass of analytic functions. Acta Math. Sin. Engl. Ser. 30, 1133–1144 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Liu, J.-L., Srivastava, H.M., Yuan, Y.: A family of meromorphically functions which are starlike with respect to \(k\)-symmetric points. J. Math. Inequal. 11, 781–798 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Mishra, A.K., Panigrahi, T., Mishra, R.K.: Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking. Math. Comput. Model. 57, 945–962 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Nunokawa, M., Srivastava, H.M., Tuneski, N., Jolevska-Tuneska, B.: Some Marx-Strohhäcker type results for a class of multivalent functions. Miskolc Math. Notes 18, 353–364 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pavatham, R., Radha, S.: On \(\alpha \)-starlike and \(\alpha \)-close-to-convex functions with respect to \(n\)-symmetric points. Indian J. Pure Appl. Math. 16, 1114–1122 (1986)MathSciNetGoogle Scholar
  15. 15.
    Peng, Z.-G., Han, Q.-Q.: On the coefficients of several classes of bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed. 34, 228–240 (2014)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Sokol, J.: A certain class of starlike functions. Comput. Math. Appl. 62, 611–619 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Srivastava, H.M., El-Ashwah, R.M., Breaz, N.: A certain subclass of multivalent functions involving higher-order derivatives. Filomat 30, 113–124 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Srivastava, H.M., Gaboury, S., Ghanim, F.: Coefficient estimates for some general subclasses of analytic and bi-univalent functions. Afrika Mat. 28, 693–706 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Srivastava, H.M., Joshi, S.B., Joshi, S.S., Pawar, H.: Coefficient estimates for certain subclasses of meromorphically bi-univalent functions. Palest. J. Math 5, 250–258 (2016). (Special Issue: 1)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Srivastava, H.M., Alhindi, K.R., Darus, M.: An investigation into the polylogarithm function and its associated class of meromorphic functions. Maejo Int. J. Sci. Tech. 10, 166–174 (2016)Google Scholar
  21. 21.
    Srivastava, H.M.: D.-G. Yang and N-E. Xu, Some subclasses of meromorphically multivalent functions associated with a linear operator. Appl. Math. Comput. 195, 11–23 (2008)MathSciNetGoogle Scholar
  22. 22.
    Sun, Y., Jiang, Y.-P., Rasila, A., Srivastava, H.M.: Integral representations and coefficient estimates for a subclass of meromorphic starlike functions. Complex Anal. Oper. Theory 11, 1–19 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wang, Z.-G., Gao, C.-Y., 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)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Xu, N.-E., Yang, D.-G.: Some classes of analytic and multivalent functions involving a linear operator. Math. Comput. Model. 49, 955–965 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Yang, D.-G., Liu, J.-L.: On functions starlike with respect to \(k\)-symmetric points. Houst. J. Math. 41, 445–470 (2015)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of MathematicsYangzhou UniversityYangzhouPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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