Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator

  • 85 Accesses

  • 13 Citations

Abstract

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Ali, R. M., Ravichandran, V. and Seenivasagan, N., Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc., 31(2), 2008, 192–207.

  2. [2]

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

  3. [3]

    Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135, 1969, 429–446.

  4. [4]

    Bulboacă, T., Integral operators that preserve the subordination, Bull. Korean Math. Soc., 34, 1997, 627–636.

  5. [5]

    Bulboacă, T., A class of superordination-preserving integral operators, Indag. Math. (N. S.), 13, 2002, 301–311.

  6. [6]

    Carlson, B. C. and Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15, 1984, 737–745.

  7. [7]

    Cho, N. E. and Srivastava, H. M., Argument estimation of certain analytic functions defined by a class of multiplier transformation, Math. Comput. Modelling, 37, 2003, 39–49.

  8. [8]

    Choi, J. H., Saigo, M. and Srivastava, H. M., Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276, 2002, 432–445.

  9. [9]

    Garg, M., Jain, K. and Kalla, S. L., On generalized Hurwitz-Lerch Zeta distribution, Appl. Appl. Math., 4, 2009, 26–39.

  10. [10]

    Goyal, S. P. and Laddha, R. K., On generalized Riemann zeta function and generalized Lambert’s transform, Gan. ita Sandesh, 11, 1997, 99–108.

  11. [11]

    Goyal, S. P. and Prajapat, J. K., Certain formulas for unified Riemann Zeta and related functions, J. Rajasthan Acad. Phys. Sci., 3(4), 2004, 267–274.

  12. [12]

    Gronwall, T. H., Some remarks on conformal representation, Ann. Math., 16, 1914/1915, 72–76.

  13. [13]

    Jung, I. B., Kim, Y. C. and Srivastava, H. M., The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176, 1993, 138–147.

  14. [14]

    Miller, S. S. and Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65, 1978, 289–305.

  15. [15]

    Miller, S. S. and Mocanu, P. T., Differential subordinations and univalent functions, Michigan Math. J., 28, 1981, 157–171.

  16. [16]

    Miller, S. S. and Mocanu, P. T., Differential Subordinations, Theory and Applications, Marcel Dekker, New York, Basel, 2000.

  17. [17]

    Miller, S. S. and Mocanu, P. T., Subordinants of differential superordinations, Comp. Var. Theory Appl., 48, 2003, 815–826.

  18. [18]

    Miller, S. S., Mocanu, P. T. and Reade, M. O., Subordination-preserving integral operators, Trans. Amer. Math. Soc., 283, 1984, 605–615.

  19. [19]

    Noor, K. I. and Bukhari, S. Z. H., Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator, Integral Transforms Spec. Funct., 21(12), 2010, 907–916.

  20. [20]

    Owa, S. and Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39, 1987, 1057–1077.

  21. [21]

    Pommerenke, C., Univalent Functions, Vanderhoeck and Ruprecht, Göttingen, 1975.

  22. [22]

    Prajapat, J. K. and Goyal, S. P., Application of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions, J. Math. Inequal., 3, 2009, 129–137.

  23. [23]

    Prajapat, J. K. and Raina, R. K., New sufficient conditions for starlikeness of analytic functions involving a fractional differ-integral operator, Demonstratio Math., 18(4), 2010, 805–813.

  24. [24]

    Srivastava, H. M. and Attiya, A. A., An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct., 18(3), 2007, 207–216.

  25. [25]

    Srivastava, H. M. and Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.

  26. [26]

    Srivastava, H. M., Saxena, R. K., Pogany, T. K., et al., Integral and computational representations of the extended Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 22(7), 2011, 487–506.

  27. [27]

    Xiang, R. G., Wang, Z. G. and Darus, M., A family of integral operators preserving subordination and superordination, Bull. Malays. Math. Sci. Soc. (2), 33(1), 2010, 121–131.

Download references

Author information

Correspondence to Jugal K. Prajapat.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Prajapat, J.K., Bulboacă, T. Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator. Chin. Ann. Math. Ser. B 33, 569–582 (2012). https://doi.org/10.1007/s11401-012-0722-3

Download citation

Keywords

  • Differential subordination and superordination
  • Analytic functions, Univalent functions
  • Starlike functions
  • Convex functions
  • Srivastava-Attiya integral operator
  • Hypergeometric functions

2000 MR Subject Classification

  • 30C80
  • 30C45