Classes of Multivalent Spirallike Functions Associated with Symmetric Regions

Abstract

We define a function to unify the well-known class of Janowski functions with a class of spirallike functions of reciprocal order. We focus on the impact of defined function on various conic regions which are symmetric with respect to the real axis. Further, we have defined a new subclass of multivalent functions of complex order subordinate to the extended Janowski function. This work bridges the studies of various subclasses of spirallike functions and extends well-known results. Interesting properties have been obtained for the defined function class. Several consequences of our main results have been pointed out.

Keywords

• multivalent functions
• Jackson’s <i>q</i>-derivative operator
• reciprocal class
• starlike functions
• convex functions
• subordination