DOI QR코드

DOI QR Code

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASS FOR SPIRALLIKE FUNCTIONS DEFINED BY MEANS OF GENERALIZED ATTIYA-SRIVASTAVA OPERATOR

  • Yavuz, Tugba (Department of Mathematics Gebze Technical University)
  • 투고 : 2015.05.18
  • 발행 : 2016.10.31

초록

In this article, we derive a sharp estimates for the Taylor-Maclaurin coefficients of functions in some certain subclasses of spirallike functions which are defined by generalized Srivastava-Attiya operator. Several corollaries and consequences of the main result are also considered.

키워드

참고문헌

  1. J. W. Alexander, Functions which map the interior of the unit circle upon simple region, Ann. Math. 17 (1915), no. 1, 12-22. https://doi.org/10.2307/2007212
  2. S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
  3. L. Bieberbach, Uber die Koeffizienten der einigen Potenzreihen welche eine schlichte Abbildung des Einheitskreises vermitten, S. B. Preuss. Akad. Wiss. 1: Sitzungsb. Berlin 38 (1916), 940-955.
  4. L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137-152. https://doi.org/10.1007/BF02392821
  5. J. Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch zeta function, Appl. Math. Comput. 170 (2005), no. 1, 399-409. https://doi.org/10.1016/j.amc.2004.12.004
  6. C. Ferreira and J. L. Lopez, Asymptotic expansions of the Hurwitz-Lerch zeta function, J. Math. Anal. Appl. 298 (2004), no. 1, 210-224. https://doi.org/10.1016/j.jmaa.2004.05.040
  7. M. Garg, K. Jain, and H. M. Srivastava, Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch zeta functions, Integral Transforms Spec. Funct. 17 (2006), no. 11, 803-815. https://doi.org/10.1080/10652460600926907
  8. Y. C. Kim and H. M. Srivastava, Some subordination properties for spirallike functions, Appl. Math. Comput. 203 (2008), no. 2, 838-842. https://doi.org/10.1016/j.amc.2008.05.093
  9. R. J. Libera, Univalent ${\alpha}$-spiral functions, Canad. J. Math. 19 (1967), 449-456. https://doi.org/10.4153/CJM-1967-038-0
  10. S.-D. Lin and H. M. Srivastava, Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput. 154 (2004), no. 3, 725-733. https://doi.org/10.1016/S0096-3003(03)00746-X
  11. S.-D. Lin, H. M. Srivastava, and P. Y. Wang, Some expansion formulas for a class of generalized Hurwitz-Lerch zeta functions, Integral Transforms Spec. Funct. 17 (2006), no. 11, 817-827. https://doi.org/10.1080/10652460600926923
  12. G. Murugusundaramoorthy, Subordination results for spiral-like functions associated with the Srivastava-Attiya operator, Integral Transforms Spec. Funct. 23 (2012), no. 2, 97-103. https://doi.org/10.1080/10652469.2011.562501
  13. M. A. Nasr and M. K. Aouf, Radius of convexity for the class of starlike functions of complex order, Bull. Fac. Sci. Assiut Univ. A 12 (1983), no. 1, 153-159.
  14. J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the class of strongly starlike and convex functions, J. Math. Inequal. 3 (2009), no. 1, 129-137.
  15. D. Raducanu and H. M. Srivastava, A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct. 18 (2007), no. 11-12, 933-943. https://doi.org/10.1080/10652460701542074
  16. L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pest. Mat. 62 (1932), 12-19.
  17. H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 207-216. https://doi.org/10.1080/10652460701208577
  18. H. M. Srivastava and J. Choi, Series associated with the zeta and related functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.
  19. H. M. Srivastava and S. Owa, A note on certain subclasses of spiral-like functions, Rend. Sem. Mat. Univ. Padova 80 (1988), 17-24.
  20. Q.-H. Xu, C.-B. Lv, N.-C. Luo, and H. M. Srivastava, Sharp coefficient estimates for a certain general class of spirallike functions by means of differential subordination, Filomat. 27 (2013), no. 7, 1351-1356. https://doi.org/10.2298/FIL1307351X
  21. Q.-H. Xu, C.-B. Lv, and H. M. Srivastava, Coefficient estimates for the inverses of a certain general class of spirallike functions, Appl. Math. Comput. 219 (2013), no. 12, 7000-7011. https://doi.org/10.1016/j.amc.2012.12.055