An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

Abstract

In this present investigation, we will concern with the family of normalized analytic error function which is defined by

E(r)f(z) = root pi z/2 er f(root z) = z + Sigma(infinity)(n=2) (-1)(n-1)/(2n - 1)(n - 1)! z(n).

By making the use of the trigonometric polynomials U-n(p, q, e(i theta)) as well as the rule of subordination, we introduce several new classes that consist of q-starlike and q-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.