Abstract and Applied Analysis

Certain Subclasses of Multivalent Analytic Functions

Yi-Ling Cang and Jin-Lin Liu

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Abstract

Two new subclasses H p , k ( λ , A , B ) and Q p , k ( λ , A , B ) of multivalent analytic functions are introduced. Distortion inequalities and inclusion relation for H p , k ( λ , A , B ) and Q p , k ( λ , A , B ) are obtained. Some results of the partial sums of functions in these classes are also given.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 890404, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511979

Digital Object Identifier
doi:10.1155/2013/890404

Mathematical Reviews number (MathSciNet)
MR3081610

Zentralblatt MATH identifier
06704921

Citation

Cang, Yi-Ling; Liu, Jin-Lin. Certain Subclasses of Multivalent Analytic Functions. Abstr. Appl. Anal. 2013 (2013), Article ID 890404, 8 pages. doi:10.1155/2013/890404. https://projecteuclid.org/euclid.aaa/1393511979


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References

  • I. R. Nezhmetdinov and S. Ponnusamy, “On the class of univalent functions starlike with respect to $N$-symmetric points,” Hokkaido Mathematical Journal, vol. 31, no. 1, pp. 61–77,2002.
  • I. R. Nezhmetdinov, “On the order of starlikeness of the class $UST$,” Journal of Mathematical Analysis and Applications, vol. 234, no. 2, pp. 559–566, 1999.
  • R. Pavatham and S. Radha, “On $\alpha $-starlike and $\alpha $-close-to-con-vex functions with respect to n-symmetric points,” Indian Journal of Pure and Applied Mathematics , vol. 16, pp. 1114–1122, 1986.
  • S. Ponnusamy, Some applications of differential subordination and convolution techniques to univalent functions theory [Ph.D. thesis], I. I. T., Kanpur, India, 1988.
  • Z.-G. Wang, C.-Y. Gao, and S.-M. Yuan, “On certain subclasses of close-to-convex and quasi-convex functions with respect to $k$-symmetric points,” Journal of Mathematical Analysis and Applications, vol. 322, no. 1, pp. 97–106, 2006.
  • S.-M. Yuan and Z.-M. Liu, “Some properties of $\alpha $-convex and $\alpha $-quasiconvex functions with respect to $n$-symmetric points,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1142–1150, 2007.
  • M. K. Aouf and J. Dziok, “Distortion and convolutional theorems for operators of generalized fractional calculus involving Wright function,” Journal of Applied Analysis, vol. 14, no. 2, pp. 183–192, 2008.
  • J. Dziok, R. K. Raina, and J. Sokół, “On $\alpha $-convex functions related to shell-like functions connected with Fibonacci numbers,” Applied Mathematics and Computation, vol. 218, no. 3, pp. 996–1002, 2011.
  • J. Dziok, R. K. Raina, and J. Sokół, “Certain results for a class of convex functions related to a shell-like curve connected with Fibonacci numbers,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2605–2613, 2011.
  • M.-S. Liu, S. Owa, and N.-S. Song, “Properties of certain transforms defined by convolution of analytic functions,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4702–4709, 2013.
  • Q. Yang and J.-L. Liu, “Argument property for certain analytic functions,” Abstract and Applied Analysis, vol. 2012, Article ID 391038, 8 pages, 2012.