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Second order differential subordination and superordination of Liu-Srivastava operator on meromorphic functions

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Abstract

In this paper we study some applications of second order differential subordination, superordination and sandwich-type results for certain admissible classes of meromorphically multivalent functions associated with the Liu-Srivastava operator.

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References

  1. Aghalary, R., Ali, R..M., Joshi, S..B., Ravichandran, V.: Inequalities for analytic functions defined by certain linear operator. Internat. J. Math. Sci. 4(2), 267–274 (2005)

    MathSciNet  MATH  Google Scholar 

  2. Ali, R.M., Ravichandran, V., Seenivasagan, N.: Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions. Bull. Malays. Math. Sci. Soc. (2) 31(2), 193–207 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Ali, R.M., Ravichandran, V., Seenivasagan, N.: Differential subordination and superodination of analytic functions defined by the multiplier transformation. Math. Inequal. Appl. 12(1), 123–139 (2009)

    MathSciNet  MATH  Google Scholar 

  4. Ali, R.M., Ravichandran, V., Seenivasagan, N.: On subordination and superordination of the multiplier transformation for meromorphic functions. Bull. Malays. Math. Sci. Soc. 33(2), 311–324 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Aouf, M.K.: New criteria for multivalent meromorphic starlike functions of order alpha. Proc. Japan Acad. Ser. A 69, 66–70 (1993)

    Article  MathSciNet  Google Scholar 

  6. Aouf, M.K., Seoudy, T.M.: Differential subordination and superordination of analytic functions defined by an integral operator. Eur. J. Pure Appl. Math. 3(1), 26–44 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Aouf, M.K., Seoudy, T.M.: Subordination and superordination of a certain integral operator on meromorphic functions. Comput. Math. Appl. 59, 3669–3678 (2010)

    Article  MathSciNet  Google Scholar 

  8. Aouf, M.K., Seoudy, T.M.: Differential subordination and superordination of analytic functions defined by certain integral operator. Acta Univ. Apulensis 24, 211–229 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Aouf, M.K., Seoudy, T.M.: Subordination and superordination of certain linear operator on meromorphic functions. Ann. Univ. Mariae Curie-Sklodowska Sect. A 64(1), 1–16 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Aouf, M.K., Seoudy, T.M.: Some properties of certain subclasses of p-valent Bazilevic functions associated with the generalized operator. Appl. Math. Lett. 24(11), 1953–1958 (2011)

    Article  MathSciNet  Google Scholar 

  11. Aouf, M.K., Seoudy, T.M.: Classes of analytic functions related to the Dziok-Srivastava operator. Integral Transform. Spec. Funct. 22(6), 423–430 (2011)

    Article  MathSciNet  Google Scholar 

  12. Aouf, M.K., Seoudy, T.M.: Admissible classes of multivalent functions associated with Liu-Owa integral operator. Quaest. Math. 42(9), 1253–1269 (2019)

    Article  MathSciNet  Google Scholar 

  13. Aouf, M.K., Srivastava, H.M., Seoudy, T.M.: Certain admissible classes of multivalent functions. J. Complex Anal. 2014, 1–7 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Bulboacă, T.: Differential Subordinations and Superordinations, Recent Results. House of Scientific Book Publ, Cluj-Napoca (2005)

    Google Scholar 

  15. Cho, N.E., Kim, I.H.: Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function. Appl. Math. Comput. 187(1), 115–121 (2007)

    MathSciNet  MATH  Google Scholar 

  16. Dinggong, Y.: On a class of meromorphic starlike multivalent functions. Bull. Inst. Math. Acad. Sinica 24, 151–157 (1996)

    MathSciNet  MATH  Google Scholar 

  17. Dziok, J., Srivastava, H.M.: Classes of analytic functions associated with the generalized hypergeometric function. Appl. Math. Comput. 103(1), 1–13 (1999)

    Article  MathSciNet  Google Scholar 

  18. Liu, J.-L., Srivastava, H.M.: A linear operator and associated families of meromorphically multivalent functions. J. Math. Anal. Appl. 259, 151–157 (1996)

    MathSciNet  Google Scholar 

  19. Liu, J.-L., Srivastava, H.M.: Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Math. Comput. Modelling 39, 21–34 (2004)

    Article  MathSciNet  Google Scholar 

  20. Miller, S.S., Mocanu, P.T.: Differential subordinations: theory and applications, series on monographs and textbooks in pure and applied mathematics, vol. 225. Marcel Dekker, New York (2000)

    Book  Google Scholar 

  21. Miller, S.S., Mocanu, P.T.: Subordinants of differential superordinations. Complex Var. Theory Appl. 48(10), 815–826 (2003)

    MathSciNet  MATH  Google Scholar 

  22. Mohd, M.H., Darus, M.: Differential subordination and superordination for Srivastava-Attiya operator, Int. J. Differ. Equ., Vol. 2011, Art. ID 902830, 19

  23. Raina, R.K., Srivastava, H.M.: A new class of meromorphically multivalent functions with applications to generalized hypergeometric functions. Math. Comput. Modelling 43(3–4), 350–356 (2006)

    Article  MathSciNet  Google Scholar 

  24. Seoudy, T.M.: Certain properties of multivalent functions associated with the Dziok-Srivastava operator. J. Math. 2013, 1–6 (2013)

    Article  MathSciNet  Google Scholar 

  25. Seoudy, T.M., Aouf, M.K.: Classes of admissible functions associated with certain integral operators applied to meromorphic functions. Bull. Iran Math. Soc. 41(4), 793–804 (2015)

    MathSciNet  MATH  Google Scholar 

  26. Seoudy, T.M., Aouf, M.K.: On certain subclass of p-valent non-Bazilevic functions defined by the Dziok-Srivastava operator. Asian-Eur. J. Math. 6(3), 1–15 (2013)

    Article  MathSciNet  Google Scholar 

  27. Seoudy, T.M., Aouf, M.K.: A class of p-valent meromorphic functions defined by the Lui-Srivastava operator. Ukr. Math. J. 66(9), 1383–1392 (2015)

    Article  Google Scholar 

  28. Srivastava, H.M., Patel, J.: Some subclasses of multivalent functions involving a certain linear operator. J. Math. Anal. Appl. 310(1), 209–228 (2005)

    Article  MathSciNet  Google Scholar 

  29. Uralegaddi, B.A., Somanatha, C.: New criteria for meromorphic starlike univalent functions. Bull. Austral. Math. Soc. 43(1), 137–140 (1991)

    Article  MathSciNet  Google Scholar 

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The author is grateful to the referees for their valuable suggestions.

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Seoudy, T.M. Second order differential subordination and superordination of Liu-Srivastava operator on meromorphic functions. Afr. Mat. 32, 1399–1408 (2021). https://doi.org/10.1007/s13370-021-00907-4

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