ON A SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS

Year 2009, Volume: 38 Issue: 2, 95 - 101, 01.02.2009

Z.-g. Wang D.-z. Chen

Abstract

In this paper, we introduce a new subclass Ks(λ, A, B) of close-toconvex functions. Such results as inclusion relationships, coefficient estimates, distortion and covering theorems for this class are proved. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

Keywords

Analytic functions, Starlike functions, Close-to-convex functions, Hadamard product (or convolution), Subordination between analytic functions, 2000 AMS Classification: 30 C 45

ON A SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS

Abstract

References

• Gao, C. -Y. and Zhou, S. -Q. On a class of analytic functions related to the starlike functions, Kyungpook Math. J. 45, 123–130, 2005.
• Liu, M. -S. On a subclass of p-valent close-to-convex functions of order β and type α, J. Math. Study 30, 102–104, 1997 (in Chinese).
• Rogosinski, W. On the coefficients of subordinate functions, Proc. London Math. Soc. (Ser. 2) 48, 48–82, 1943.
• Wang, Z. -G., Gao, C. -Y. and Yuan, S. -M. On certain subclass of close-to-convex functions, Acta Math. Acad. Paedagog. Nyh´azi. (N.S.) 22, 171–177, 2006.
• Wu, Z. -R. The integral opterator of starlikeness and the family of Bazileviˇc functions, Acta Math. Sinica 27, 394–409, 1984 (in Chinese).