Certain Class of Bi-Univalent Functions Defined by Sălăgean <i>q</i>-Difference Operator Related with Involution Numbers

Abstract

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers.

Keywords

• univalent functions
• starlike and convex functions
• bi-univalent functions
• Sălăgean operator
• <i>q</i>-difference operator
• coefficient bounds