Subclasses of univalent functions
by
Aini Janteng
School of Science and Technology, Universiti Malaysia Sabah, Locked Bag No. 2073, 88999 Kota Kinabalu, Sabah, Malaysia
Coauthors: Suzeini Abdul Halim and Maslina Darus

We consider the class S consisting of functions which are analytic, univalent and normalised. Subclasses of S namely the classes of starlike functions with respect to other points have also been quite extensively looked at. [see Sakaguchi, ElAshwah and Thomas, Halim]. Later, the class of functions involving the expression [(zf'(z))/f(z)]+[(az²f"(z))/f(z)] were introduced. In this paper, we incorporate these two ideas and introduce new subclasses of S denoted by K_s(a, b, g), K_c(a, b, g) and K_sc(a, b, g) for 0 ≤ a < 1, 0 ≤ b < 1 and 0 ≤ g < 1. We obtain properties of functions in these classes as well as looked at the behaviour of certain integral operators.

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Date received: January 24, 2007