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

Year, pages: 2020, 599 - 604

In this present investigation, we will concern with the family of normalized analytic error function which is defined by \begin{equation*} E_rf(z)=\frac{\sqrt{π z}}{2}\er f(\sqrt{z})=z+\overset{∞}{\underset% {n=2}{∑}}(((-1)^n-1) / ((2n-1)(n-1)!))zⁿ. \end{equation*}% By making the use of the trigonometric polynomials $U_n(p,q,\e^\iiθ)$ as well as the rule of subordination, we introduce several new classes that consist of $\mathfrak{q}$-starlike and $\mathfrak{q}$-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

Altinkaya, S. 2020. An extension of $q$-starlike and $q$-convex error functions endowed with the trigonometric polynomials. In Mathematica Slovaca, vol. 70, no.3, pp. 599-604. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0374

Altinkaya, S. (2020). An extension of $q$-starlike and $q$-convex error functions endowed with the trigonometric polynomials. Mathematica Slovaca, 70(3), 599-604. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0374

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava