Skip to main content
Log in

Some Sufficient Conditions for Generalized Bessel Functions Associated with Conic Regions

  • Published:
Vietnam Journal of Mathematics Aims and scope Submit manuscript

Abstract

The purpose of the present paper is to investigate some sufficient conditions for convolution operator \(H_{k_{1,c}}f(z)=zu_{p}(z)*f(z)\) belonging to the classes k − UCV(α), kS p (α), \(S^{\ast }_{\lambda }\), and C λ .

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. Baricz, A.: Geometric properties of generalized Bessel functions. Publ. Math. Debr. 73, 155–178 (2008)

    MATH  MathSciNet  Google Scholar 

  2. Baricz, A.: Geometric properties of generalized Bessel functions of complex order. Math. 48(71), 13–18 (2006)

    MathSciNet  Google Scholar 

  3. Baricz, A.: Bessel transforms and Hardy space of generalized Bessel functions. Math. 48(71), 127–136 (2006)

    MathSciNet  Google Scholar 

  4. Baricz, A.: Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics vol. 1994. Springer-Verlag, Berlin (2010)

    Google Scholar 

  5. Baricz, A.: Generalized Bessel Functions of the First Kind. Ph.D. Thesis. Babes-Bolyai University, Cluj-Napoca (2008)

    Google Scholar 

  6. Bharati, R., Parvatham, R., Swaminathan, A.: On subclasses of uniformly convex functions and corresponding class of starlike functions. Tamkang J. Math. 28, 17–32 (1997)

    MATH  MathSciNet  Google Scholar 

  7. Dixit, K.K., Porwal, S.: On a certain class of k-uniformly convex functions with negative coefficients. Bull. Cal. Math. Soc. 100, 639–652 (2008)

    MATH  MathSciNet  Google Scholar 

  8. Gangadharan, A., Shanmugam, T.N., Srivastava, H.M.: Generalized hypergeometric function associated with k-uniformly convex functions. Comput. Math. Appl. 44, 1515–1526 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Goodman, A.W.: On uniformly convex functions. Ann. Polon. Math. 56, 87–92 (1991)

    MATH  MathSciNet  Google Scholar 

  10. Goodman, A.W.: On uniformly starlike functions. J. Math. Anal. Appl. 155, 364–370 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kanas, S.: Differential subordination related to conic sections. J. Math. Anal. Appl. 317, 650–658 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Kanas, S., Srivastava, H.M.: Linear operators associated with k-uniformly convex functions. Int. Trans. Spec. Funct. 9, 121–132 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kanas, S., Sugawa, T.: On conformal representation of the interior of an ellipse. Ann. Acad. Sci. Fenn. Math. 31, 329–348 (2006)

    MATH  MathSciNet  Google Scholar 

  14. Kanas, S., Wisinowaska, A.: Conic regions and k-uniform convexity. J. Comput. Appl. Math. 105, 327–336 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kanas, S., Wisniowska, A.: Conic regions and k-starlike functions. Rev. Roum. Math. Pure Appl. 45, 647–657 (2000)

    MATH  MathSciNet  Google Scholar 

  16. Ma, W., Minda, D.: Uniformly convex functions. Ann. Polon. Math. 57, 165–175 (1992)

    MATH  MathSciNet  Google Scholar 

  17. Ponnusamy, S., Rønning, F.: Starlike properties for convolutions involving hypergeometric series. Ann. Univ. Mariae Curie-Sklodawska SK. Todawaska L.II 1(16), 141–155 (1998)

    Google Scholar 

  18. Porwal, S.: Mapping properties of generalized Bessel functions on some subclasses of univalent functions. Anal. Univ. Oradea Fasc. Mat. XX, 51–60 (2013)

  19. Porwal, S., Dixit, K.K.: An application of generalized Bessel functions on certain analytic functions. Acta Univ. Matthiae Belii, ser Math., 51–57 (2013)

  20. Robertson, M.S.: On the theory of univalent functions. Ann. Math. 37, 374–408 (1936)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Sharma, A.K., Porwal, S., Dixit, K.K.: Class mappings properties of convolutions involving certain univalent functions associated with hypergeometric functions. J. Math. Anal. Appl 1, 326–333 (2013)

    Google Scholar 

  23. Silverman, H.: Univalent functions with negative coefficients. Proc. Amer. Math. Soc. 51, 109–116 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  24. Srivastava, H.M., Mishra, A.K.: Applications of fractional calculus to parabolic starlike and uniformly convex functions. Comput. Math. Appl 39, 57–69 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. Swaminathan, A.: Certain sufficiency conditions on Gaussian hypergeometric functions. J. Inequal. Pure Appl. Math. 5, 83 (2004)

    MathSciNet  Google Scholar 

Download references

Acknowledgment

The authors are thankful to the referee for his/her valuable comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saurabh Porwal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Porwal, S., Ahmad, M. Some Sufficient Conditions for Generalized Bessel Functions Associated with Conic Regions. Vietnam J. Math. 43, 163–172 (2015). https://doi.org/10.1007/s10013-014-0089-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10013-014-0089-8

Keywords

Mathematics Subject Classification (2010)

Navigation