Skip to main content
Log in

Integral Operators Preserving Subordination and Superordination for Multivalent Functions

  • Published:
Ukrainian Mathematical Journal Aims and scope

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on multivalent functions. The sandwich-type theorem for these integral operators is also derived. Moreover, our results extend some earlier results. Combining these new theorems with some previous related results, we give interesting subordination and superordination consequences for a wide class of analytic integral operators.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. Bulboacă, “Integral operators that preserve the subordination,” Bull. Korean Math. Soc., 32, 627–636 (1997).

    MathSciNet  MATH  Google Scholar 

  2. T. Bulboacă, “On a class of integral operators that preserve the subordination,” Pure Math. Appl. (PU.M.A.), 13, 87–96 (2002).

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. T. Bulboacă, “Sandwich-type theorems for a class of integral operators,” Bull. Belg. Math. Soc. Simon Stevin, 13, No. 3, 537–550 (2006).

    Article  MathSciNet  Google Scholar 

  5. T. Bulboacă, “Sandwich-type results for a class of convex integral operators,” Acta Math. Sci. Ser. B (Engl. Ed.), 32, No. 3, 989–1001 (2012).

    MathSciNet  MATH  Google Scholar 

  6. N. E. Cho and T. Bulboacă, “Subordination and superordination properties for a class of integral operators,” Acta Math. Sin. (Engl. Ser.), 26, No. 3, 515–522 (2010).

    Article  MathSciNet  Google Scholar 

  7. T. H. Gronwall, “Some remarks on conformal representation,” Ann. of Math. (2), 16, No. 1-4, 72–76 (1914–1915).

  8. S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Michigan Math. J., 28, No. 2, 157–172 (1981).

    Article  MathSciNet  Google Scholar 

  9. S. S. Miller and P. T. Mocanu, “Univalent solutions of Briot–Bouquet differential equations,” J. Different. Equat., 56, No. 3, 297–309 (1985).

    Article  MathSciNet  Google Scholar 

  10. S. S. Miller and P. T. Mocanu, “Integral operators on certain classes of analytic functions,” Univalent Functions, Fractional Calculus and their Applications (Kōriyama, 1988), Ellis Horwood Ser. Math. Appl., Horwood, Chichester (1989), p. 153–166.

  11. S. S. Miller and P. T. Mocanu, “Classes of univalent integral operators,” J. Math. Anal. Appl., 157, No. 1, 147–165 (1991).

    Article  MathSciNet  Google Scholar 

  12. S. S. Miller and P. T. Mocanu, “Differential subordinations. Theory and applications,” Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York (2000).

  13. S. S. Miller and P. T. Mocanu, “Subordinants of differential superordinations,” Complex Var. Theory Appl., 48, No. 10, 815–826 (2003).

    MathSciNet  MATH  Google Scholar 

  14. Ch. Pommerenke, Univalent Functions, Studia Mathematica/Mathematische Lehrbü cher, Band XXV, Vandenhoeck & Ruprecht, Göttingen (1975).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. M. Seoudy.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 749–762, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.437.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouf, M.K., Bulboacă, T. & Seoudy, T.M. Integral Operators Preserving Subordination and Superordination for Multivalent Functions. Ukr Math J 73, 872–887 (2021). https://doi.org/10.1007/s11253-021-01965-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-021-01965-4

Navigation