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

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined byErf(z)=πz2erf(z)=z+∑n=2∞(−1)n−1(2n−1)(n−1)!zn.$$\begin{array}{}\displaystyleE_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset{n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}.\end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematica Slovaca de Gruyter

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

Mathematica Slovaca, Volume 70 (3): 6 – Jun 25, 2020
6 pages

/lp/de-gruyter/an-extension-of-q-starlike-and-q-convex-error-functions-endowed-with-4QvNREGI1u
Publisher
de Gruyter
ISSN
0139-9918
eISSN
1337-2211
DOI
10.1515/ms-2017-0374
Publisher site
See Article on Publisher Site

### Abstract

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined byErf(z)=πz2erf(z)=z+∑n=2∞(−1)n−1(2n−1)(n−1)!zn.$$\begin{array}{}\displaystyleE_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset{n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}.\end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) 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.

### Journal

Published: Jun 25, 2020

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