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

Abstract

<jats:title>Abstract</jats:title><jats:p>In this present investigation, we will concern with the family of normalized analytic error function which is defined by</jats:p><jats:p><jats:disp-formula id="j_ms-2017-0374_eq_001_w2aab3b7d491b1b6b1aab1c14b2aAa"><jats:alternatives><jats:tex-math>$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$</jats:tex-math></jats:alternatives></jats:disp-formula></jats:p><jats:p>By making the use of the trigonometric polynomials <jats:italic>U<jats:sub>n</jats:sub></jats:italic>(<jats:italic>p</jats:italic>, <jats:italic>q</jats:italic>, e<jats:sup>i<jats:italic>θ</jats:italic></jats:sup>) 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.</jats:p>