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

Year 2012, Volume: 41 Issue: 5, 635 - 642, 01.05.2012

Erhan Deniz

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

• Duren, P. L. Univalent Functions (Springer-Verlag, New York, 1983).
• Goodman, A. W. Univalent Functions, Volume I (Polygonal, Washington, 1983).
• Jack, I. S. Functions starlike aud convex of order α, J. London Math. Soc. 3 (2), 469–474, 1971 .
• Irmak, H. Certain inequalities and their applications to multivalently analytic functions, Math. Inequal.Appl. 8 (3), 451–458, 2005.
• Irmak, H. and C¸ etin, ¨O. F. Some inequalities on p-valent functions, Hacet. Bull. Nat. Sci. Eng. Ser. B 28, 71–76, 1999.
• Miller, S. S. and Mocanu P. T. Second order differential inequalities in complex plane, J. Math. Anal. Appl. 65, 289–305, 1978.
• 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.
• Singh, V. and Tuneski, N. On criteria for starlikeness and convexity of analytic functions, Acta Mathematica Scientia. Series B 24 (4), 597–602, 2004.
• Srivastava, H. M. and Owa, S. (Editors) Current Topics in Analytic Function Theory (World Scientific, Singapore, 1992).
• Tuneski, N. On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248-249, 200–203, 2003.
• Wang, Z. -G. and Xu, N. A new criterion for multivalent starlike functions, Appl. Anal. Discrete Math. 2, 183–188, 2008.