New characterization of the class of starlike functions
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 615-620
Printed December 1, 2008
Emel Yavuz, Ya\c{s}ar Polato\~{g}lu, and Shigeyoshi Owa
TC \.{I}stanbul K\"{u}lt\"{u}r University, TC \.{I}stanbul K\"{u}lt\"{u}r University, and Kinki University
Abstract : For analytic functions $f(z)$ in the open unit disc $\mathbb{D}$, an operator $\mathcal{N}_{\alpha}(f(z))$ relating with starlike functions is introduced. The object of the present paper is to discuss some properties of the operator $\mathcal{N}_{\alpha}(f(z))$.
Keywords : Carath\'{e}odory function, starlike function, operator
MSC numbers : Primary 30C45
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