117
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Sufficient conditions for strongly star-like functions involving the generalized Srivastava–Attiya operator

Pages 79-90 | Received 04 Jul 2009, Accepted 30 May 2010, Published online: 04 Aug 2010

References

  • Alexander , J. W. 1915 . Functions which map the interior of the unit circle upon simple regions . Ann. Math. Ser. , 2 17 : 12 – 22 .
  • Attiya , A. A. 2007 . On a generalization class of bounded starlike functions of complex order . Appl. Math. Comput. , 187 : 62 – 67 .
  • Bernardi , S. D. 1969 . Convex and starlike univalent functions . Trans. Am. Math. Soc. , 135 : 429 – 446 .
  • Cho , N. E. , Kwon , O. S. and Srivastava , H. M. 2010 . Strong differential subordination and superordination for multivalently meromorphic functions involving the Liu–Srivastava operator . Integral Transforms Spec. Funct. , 21 : 589 – 601 .
  • Choi , J. and Srivastava , H. M. 2005 . Certain families of series associated with the Hurwitz–Lerch Zeta function . Appl. Math. Comput. , 170 : 399 – 409 .
  • Choi , J. and Srivastava , H. M. 2009 . Integral representations for the Gamma function, the Beta function, and the double Gamma function . Integral Transforms Spec. Funct. , 20 : 859 – 869 .
  • Ferreira , C. and López , J. L. 2004 . Asymptotic expansions of the Hurwitz–Lerch Zeta function . J. Math. Anal. Appl. , 298 : 210 – 224 .
  • Garg , M. , Jain , K. and Srivastava , H. M. 2006 . Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions . Integral Transforms Spec. Funct. , 17 : 803 – 815 .
  • Jung , I. B. , Kim , Y. C. and Srivastava , H. M. 1993 . The Hardy space of analytic functions associated with certain one-parameter families of integral operators . J. Math. Anal. Appl. , 176 : 138 – 147 .
  • Libera , R. J. 1969 . Some classes of regular univalent functions . Proc. Am. Math. Soc. , 16 : 755 – 758 .
  • Lin , S.-D. and Srivastava , H. M. 2004 . Some families of the Hurwitz–Lerch Zeta functions and associated fractional derivative and other integral representations . Appl. Math. Comput. , 154 : 725 – 733 .
  • Lin , S.-D. , Srivastava , H. M. and Wang , P.-Y. 2006 . Some expansion formulas for a class of generalized Hurwitz–Lerch Zeta functions . Integral Transforms Spec. Funct. , 17 : 817 – 827 .
  • Liu , J.-L. 2001 . The Noor integral and strongly starlike functions . J. Math. Anal. Appl. , 261 : 441 – 447 .
  • Liu , J.-L. 2008 . Subordinations for certain multivalent analytic functions associated with the generalized Srivastava–Attiya operator . Integral Transforms Spec. Funct. , 19 : 893 – 901 .
  • Liu , J.-L. and Srivastava , H. M. 2009 . A class of multivalently analytic functions associated with the Dziok–Srivastava operator . Integral Transforms Spec. Funct. , 20 : 401 – 417 .
  • Luo , Q.-M. and Srivastava , H. M. 2005 . Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials . J. Math. Anal. Appl. , 308 : 290 – 302 .
  • Miller , S. S. and Mocanu , P. T. 2000 . Differential Subordinations: Theory and Applications , New York : Marcel Dekker . Series in Pure and Applied Mathematics, No. 225
  • Orhan , H. and Raducanu , D. 2009 . Fekete–Szego problem for strongly starlike functions associated with generalized hypergeometric functions . Math. Comput. Modelling , 50 : 430 – 438 .
  • Prajapat , J. K. , Raina , R. K. and Srivastava , H. M. 2007 . Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators . Integral transforms Spec. Funct. , 18 : 639 – 651 .
  • Rǎducanu , D. and Srivastava , H. M. 2007 . A new class of analytic functions defined by means of a convolution operator involving the Hurwitz–Lerch Zeta function . Integral Transforms Spec. Funct. , 18 : 933 – 943 .
  • Shanmugam , T. N. , Sivasubramanian , S. and Owa , S. 2010 . On sandwich results for some subclasses of analytic functions involving certain linear operator . Integral Transforms Spec. Funct. , 21 : 1 – 11 .
  • Srivastava , H. M. and Attiya , A. A. 2007 . An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination . Integral Transforms Spec. Funct. , 18 : 207 – 216 .
  • Srivastava , H. M. and Choi , J. 2001 . Series Associated with the Zeta and Related Functions , Dordrecht, Boston, London : Kluwer Academic Publishers .
  • Srivastava , H. M. , Eker , S. S. and Seker , B. 2009 . Inclusion and neighborhood properties for certain classes of multivalently analytic functions of complex order associated with the convolution structure . Appl. Math. Comput. , 212 : 66 – 71 .
  • Srivastava , H. M. , Yang , D.-G. and Xu , N.-E. 2009 . Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator . Integral Transforms Spec. Funct. , 20 : 581 – 606 .
  • Wang , Z.-G. , Jiang , Y.-P. and Srivastava , H. M. 2009 . Some subclasses of meromorphically multivalent functions associated with the generalized hypergometric function . Comput. Math. Appl. , 57 : 571 – 586 .
  • Wang , Z.-G. , Li , Q.-G. and Jiang , Y.-P. 2010 . Certain subclasses of multivalent analytic functions involving the generalized Srivastava–Attiya operator . Integral Transforms Spec. Funct. , 21 : 221 – 234 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.