On P-Valently Close-To-Convex, Starlike and Convex Functions

Abstract

On P-Valently Close-To-Convex, Starlike and Convex Functions

Abstract

The main object of the present paper is to derive several sufficient conditions for close-to-convexity, starlikeness, and convexity of certain p-valent analytic functions in the unit disk. Some interesting consequences of the main results are also mentioned.

Keywords

• P-valent analytic functions,Starlike functions,Close-to-convex functions,Convex functions,2000 AMS Classification: 30 C 45

References

1. Duren, P. L. Univalent Functions (Springer-Verlag, New York, 1983).
2. Goodman, A. W. Univalent Functions, Volume I (Polygonal, Washington, 1983).
3. Jack, I. S. Functions starlike aud convex of order α, J. London Math. Soc. 3 (2), 469–474, 1971 .
4. Irmak, H. Certain inequalities and their applications to multivalently analytic functions, Math. Inequal.Appl. 8 (3), 451–458, 2005.
5. Irmak, H. and C¸ etin, ¨O. F. Some inequalities on p-valent functions, Hacet. Bull. Nat. Sci. Eng. Ser. B 28, 71–76, 1999.
6. Miller, S. S. and Mocanu P. T. Second order differential inequalities in complex plane, J. Math. Anal. Appl. 65, 289–305, 1978.
7. Nunokawa, M. On the theory of multivalent functions, Tsukuba J. Math. 11, 273–286, 1987. [8] Owa, S., Nunokawa, M., Saitoh, H. and Srivastava, H. M. Close-to-convexity, starlikeness, and convexity of certain analytic functions, Appl. Math. Lett. 15, 63–69, 2002.
8. Singh, V. and Tuneski, N. On criteria for starlikeness and convexity of analytic functions, Acta Mathematica Scientia. Series B 24 (4), 597–602, 2004.

9. Srivastava, H. M. and Owa, S. (Editors) Current Topics in Analytic Function Theory (World Scientific, Singapore, 1992).
10. Tuneski, N. On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248-249, 200–203, 2003.
11. Wang, Z. -G. and Xu, N. A new criterion for multivalent starlike functions, Appl. Anal. Discrete Math. 2, 183–188, 2008.