Skip to main content
Log in

Second-Order Differential Subordinations on a Class of Analytic Functions Defined by the Rafid Operator

  • Published:
Ukrainian Mathematical Journal Aims and scope

We introduce a new class of analytic functions by using the Rafid integral operator and obtain some subordination results.

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. A. Akgül, “On second-order differential subordinations for a class of analytic functions defined by convolution,” J. Nonlin. Sci. Appl., 10, No. 3, 954–963 (2017).

    Article  MathSciNet  Google Scholar 

  2. W. G. Athsan and R. H. Buti, “Fractional calculus of a class of univalent functions,” Eur. J. Pure Appl. Math., 4, No. 2, 162–173 (2011).

    MathSciNet  Google Scholar 

  3. A. Alb. Lupas, “Certain differential subordinations using Sălăgeăn and Ruscheweyh operators,” Acta Univ. Apulensis Math. Inform., No. 29, 125–129 (2012).

  4. S. Bulut, “Some applications of second-order differential subordination on a class of analytic functions defined by Komatu integral operator,” ISRN Math. Anal., No. 5, Art. ID 606235 (2014).

  5. D. J. Hallenbeck and S. Ruscheweyh, “Subordinations by convex functions,” Proc. Amer. Math. Soc., 52 (1975).

  6. S. S. Miller and P. T. Mocanu, “Differential subordinations: theory and applications,” in: Pure Appl. Math. Series Monogr. Textbooks, CRC Press (2000), 225.

  7. G. Oros and G. I. Oros, “A class of holomorphic functions II,” Lib. Math. (N.S.), 23, 65–68 (2003).

    MathSciNet  MATH  Google Scholar 

  8. G. I. Oros and G. Oros, “On a class of univalent functions defined by a generalized Sălăgean operator,” Complex Var. Elliptic Equat., 53, No. 9, 869–877 (2008).

    Article  Google Scholar 

  9. G. Sălăgean, “Subclass of univalent functions,” in: Complex Anal. (Fifth Romanian-Finnish Sem. Pt 1 (Bucharest, 1981)): Lect. Notes Math., Springer, 1013 (1981), pp. 362–372.

  10. S. S. Miller and P. T. Mocanu, “Second order differential inequalities in the complex plane,” J. Math. Anal. Appl., 65, No. 2, 298–305 (1978).

    Article  MathSciNet  Google Scholar 

  11. S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Michigan Math. J., 28, No. 2, 157–171 (1981).

    Article  MathSciNet  Google Scholar 

  12. T. Bulboacă, “Differential subordinations and superordinations,” in: Recent Results, House Sci. Book Publ., Cluj-Napoca (2005).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 5, pp. 587–598, May, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akgül, A. Second-Order Differential Subordinations on a Class of Analytic Functions Defined by the Rafid Operator. Ukr Math J 70, 673–686 (2018). https://doi.org/10.1007/s11253-018-1525-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-018-1525-9

Navigation