Skip to main content

Advertisement

SpringerLink
Log in

Some radius problems related to a certain subclass of analytic functions

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

For real parameters α and β such that 0 ≤ α < 1 < β, we denote by S(α, β) the class of normalized analytic functions which satisfy the following two-sided inequality:

$\alpha < \Re \left( {\frac{{zf'(z)}} {{f(z)}}} \right) < \beta ,z \in \mathbb{U} $

where \(\mathbb{U}\) denotes the open unit disk. We find a sufficient condition for functions to be in the class S(α, β) and solve several radius problems related to other well-known function classes.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amer, A., Darus, M.: On radius problems in the class of univalent functions. Internat. J. Pure Appl. Math., 73, 471–476 (2011)

    MATH  MathSciNet  Google Scholar 

  2. Aouf, M. K., Dziok, J., Sokół, J.: On a subclass of strongly starlike functions. Appl. Math. Lett., 24, 27–32 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. Duren, P. L.: Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983

    Google Scholar 

  4. Kobashi, H., Kuroki, K., Owa, S.: Notes on radius problems of certain univalent functions. Gen. Math., 17(4), 5–12 (2009)

    MATH  MathSciNet  Google Scholar 

  5. Kuroki, K., Owa, S.: Notes on new class for certain analytic functions. RIMS Kôkyûroku, 1772, 21–25 (2011)

    Google Scholar 

  6. MacGregor, T. H.: A subordination for convex functions of order α. J. London Math. Soc. (Se. 2), 9, 530–536 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  7. Miller, S. S., Mocanu, P. T.: Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker Incorporated, New York and Basel, 2000

    Google Scholar 

  8. Noor, K. I., Arif, M.: Some radius problems for certain classes of analytic functions with fixed second coefficients. Nonl. Funct. Anal. Appl., 15, 79–85 (2010)

    MATH  MathSciNet  Google Scholar 

  9. Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc., 118, 189–196(1993)

    Article  MathSciNet  Google Scholar 

  10. Sokół, J.: Coefficient estimates in a class of strongly starlike functions. Kyungpook Math. J., 49, 349–353 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sokół, J.: Radius problems in the class SL*. Appl. Math. Comput., 214, 569–573 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Uyanik, N., Owa, S.: Note on radius problems for certain class of analytic functions. Fract. Calc. Appl. Anal., 13, 553–560 (2010)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kyungsung University, Busan, 608-736, Republic of Korea

    Oh Sang Kwon & Young Jae Sim

  2. Department of Applied Mathematics, Pukyung National University, Busan, 608-737, Republic of Korea

    Nak Eun Cho

  3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada

    H. M. Srivastava

Authors
  1. Oh Sang Kwon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Young Jae Sim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nak Eun Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. M. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. M. Srivastava.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kwon, O.S., Sim, Y.J., Cho, N.E. et al. Some radius problems related to a certain subclass of analytic functions. Acta. Math. Sin.-English Ser. 30, 1133–1144 (2014). https://doi.org/10.1007/s10114-014-3100-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-014-3100-0

Keywords

MR(2010) Subject Classification

Search

Navigation