# Some class of analytic functions related to conic domains

In: Mathematica Slovaca, vol. 64, no. 5
Stanisława Kanas - Dorina Răducanu

## Details:

Year, pages: 2014, 1183 - 1196
Keywords:
analytic functions, starlike, convex, uniformly convex functions, $q$-derivative operator, conic sections
For $q\in (0,1)$ let the $q$-difference operator be defined as follows
$$∂qf(z)=((f(qz)-f(z)) / (z(q-1))) (z\in\mathbb{U}),$$
where $\mathbb{U}$ denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator $Rqλf$ is defined. Applying $Rqλf$ a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.