On Geometric Properties of a Certain Analytic Function with Negative Coefficients

Abstract

Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions of the form f(z)=z−∑m=2t[ω(2+β)+cγ−σ]Cm[mσ−cω(2+β)+cγ]Knzm−∑k=t+1∞akzk is defined using a generalized differential operator. Furthermore, some geometric properties for the class were established.

Keywords

• analytic functions
• univalent function
• coefficient estimates
• fixed coefficients
• extreme points