IJPAM: Volume 30, No. 2 (2006)

FUNCTIONS CLOSE-TO-CONVEX AND QUASI-CONVEX
WITH RESPECT TO OTHER POINTS

Aini Janteng$^1$, Suzeini Abdul Halim$^2$, Maslina Darus$^3$
$^{1,2}$Institute of Mathematical Sciences
University Malaya
Kuala Lumpur, 50603, MALAYSIA
$^1$e-mail: aini_jg@ums.edu.my
$^2$e-mail: suzeini@um.edu.my
$^3$School of Mathematical Sciences
Faculty of Sciences and Technology
University Kebangsaan Malaysia
Bangi, Selangor, 43600, MALAYSIA
$^3$e-mail: maslina@pkrisc.cc.ukm.my


Abstract.In [#!Sakaguchi!#], Sakaguchi introduced the class of functions starlike with respect to symmetric points. Then, El-Ashwah and Thomas in [#!El-Ashwah!#], introduced two more classes, namely starlike with respect to conjugate points and starlike with respect to symmetric conjugate points. Das and Singh in [#!Das!#], considered the class of functions convex and close-to-convex with respect to symmetric points, respectively. This paper considers other classes, namely functions close-to-convex with respect to conjugate points and functions close-to-convex with respect to symmetric conjugate points. Next, the classes of functions quasi-convex with respect to symmetric points, with respect to conjugate points and with respect to symmetric conjugate points are introduced. We give some properties for functions belonging to these classes. The behaviour of certain integral operators are also considered.

Received: June 13, 2006

AMS Subject Classification: 30C45

Key Words and Phrases: starlike with respect to symmetric points, convex with respect to symmetric points, close-to-convex with respect to symmetric points, integral operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 2