# IJPAM: Volume 30, No. 2 (2006)

**FUNCTIONS CLOSE-TO-CONVEX AND QUASI-CONVEX**

WITH RESPECT TO OTHER POINTS

WITH RESPECT TO OTHER POINTS

Institute of Mathematical Sciences

University Malaya

Kuala Lumpur, 50603, MALAYSIA

e-mail: aini_jg@ums.edu.my

e-mail: suzeini@um.edu.my

School of Mathematical Sciences

Faculty of Sciences and Technology

University Kebangsaan Malaysia

Bangi, Selangor, 43600, MALAYSIA

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