DOI QR코드

DOI QR Code

SOME RADIUS RESULTS OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE SRIVASTAVA-ATTIYA OPERATOR

  • Kim, Yong Chan (Department of Mathematics Education, Yeungnam University) ;
  • Choi, Jae Ho (Department of Mathematics Education, Daegu National University of Education)
  • 투고 : 2020.09.24
  • 심사 : 2021.02.10
  • 발행 : 2021.06.15

초록

The main object of the present paper is to investigate some radius results of the functions f(z) = z + Σn=2 anzn(|z| < 1) with |an| ≤ n for all n ∈ ℕ. Some applications for certain operator defined through convolution are also considered.

키워드

과제정보

The authors would like to express their sincere thanks to the referee for his insightful suggestions to improve the paper in current form.

참고문헌

  1. J.W. Alexander, Functions which map the interior of the unit corcle upon simple regions, Ann. Math. Ser., 2(17) (1915), 12-22. https://doi.org/10.2307/2007212
  2. L. de Branges, A proof of the Bieberbach conjecture, Acta Math., 154 (1985), 137-152. https://doi.org/10.1007/BF02392821
  3. P.L. Duren, Univalent Function, Grundlehren der Mathematischen Wissenschaften 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  4. C. Ferreira and J.L. Lopez, Asymptotic expansions of the Hurwitz-Lerch Zeta function, J. Math. Anal. Appl., 298 (2004), 210-224. https://doi.org/10.1016/j.jmaa.2004.05.040
  5. T.M. Flett, The dual of an inequality of Hardy and Littlewood and some related ineqalities, J. Math. Anal. Appl., 38 (1972), 746-765. https://doi.org/10.1016/0022-247X(72)90081-9
  6. D.J. Hallenbeck, Convex hulls and extreme points of some families of univalent functions, Trans. Amer. Math. Soc., 192 (1974), 285-292. https://doi.org/10.1090/S0002-9947-1974-0338338-8
  7. I.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176 (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
  8. Y.C. Kim and M. Nunokawa, On some radius results for certain analytic functions, Kyungpook Math. J., 37 (1997), 61-65.
  9. J.L. Liu, Sufficient conditions for strongly starlike functions involving the generalized Srivastava-Attiya operator, Intergal Transforms Spec. Funct., 22 (2011), 79-90. https://doi.org/10.1080/10652469.2010.498110
  10. S.D. Lin, H.M. Srivastava and P.Y. Wang, Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions, Intergal Transforms Spec. Funct., 17 (2006), 817-827. https://doi.org/10.1080/10652460600926923
  11. T.H. MacGregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc., 104 (1962), 532-537. https://doi.org/10.1090/S0002-9947-1962-0140674-7
  12. G. Murugusundaramoorthy, Subordination results for spiral-like functions associated with the Srivastava-Attiya operator, Intergal Transforms Spec. Funct., 23 (2012), 97-103. https://doi.org/10.1080/10652469.2011.562501
  13. G.S. Salagean, Subclasses of Univalent Functions, Lecture Notes in Mathematics, Vol. 1013, Springer, Berlin, 1983, pp. 362-372.
  14. H.M. Srivastava and A.A. Attiya, An integral operator associated with thw HurwitzLerch Zeta function and differential subordination, Intergal Transforms Spec. Funct., 18 (2007), 207-216. https://doi.org/10.1080/10652460701208577
  15. H.M. Srivastava and J. Choi, Series Associated with the Zeta and Related Function, Kluwer Academic Publishers, Dordrecht, 2001.
  16. H.M. Srivastava, D. Jankov, T.K. Pog'any and R.K. Saxena, Two-side inequalities for the extended Hurwitz-Lerch Zeta function, Comput. Math. Appl., 62 (2011), 516-522. https://doi.org/10.1016/j.camwa.2011.05.035
  17. A.K. Wanas, J. Choi and N.E. Cho, Geometric properties for a family of holomorpic functions associated with Wanas operator defined on complex Hilbert space, Asian-European J. Math., (2020), doi:10.1142/s1793557121501229.
  18. S.M. Yuan and Z.M. Liu, Some properties of two subclasses of k-fold symmetric functions associated with Srivastava-Attiya operator, Appl. Math. Comput., 218 (2011), 1136-1141. https://doi.org/10.1016/j.amc.2011.03.080