Some inequalities on Bazilevic class of functions involving quasi-subordination

Quasi-subordination which is an extension of the majorization and subordination principle, has been used to define a subclass of Bazilevic functions of complex order. Various classes of analytic functions that map unit disc onto conic domains and some classes of special functions are studied in dual. Inequalities for the initial Taylor-Maclaurin coefficients and unified solution of Fekete-Szego problem for subclasses of analytic functions related to various conic regions are our main results. Our main results have many applications which are presented in the form of corollaries.

Automated summary

The concept of quasi-subordination is introduced to study a subclass of Bazilevic functions of complex order and analytic functions mapping the unit disc onto conic domains. The main results include inequalities for the initial Taylor-Maclaurin coefficients and a unified solution to the Fekete-Szego problem for subclasses of analytic functions related to various conic regions. These results have many practical applications, presented in the form of corollaries.