Properties for a Certain Subclass of Analytic Functions Associated with the Salagean <i>q</i>-Differential Operator

Abstract

Using the Salagean q-differential operator, we investigate a novel subclass of analytic functions in the open unit disc, and we use the Hadamard product to provide some inclusion relations. Furthermore, the coefficient conditions, convolution properties, and applications of the q-fractional calculus operators are investigated for this class of functions. In addition, we extend the Miller and Mocanu inequality to the q-theory of analytic functions.

Keywords

• <i>q</i>-fractional calculus operators
• <i>q</i>-difference operator
• <i>q</i>-Salagean differential operator
• <i>q</i>-integral operator
• inclusion relations
• analytic function