### Subclasses of Analytic Functions with Respect to Symmetric and Conjugate Points Connected with the $q$-Borel Distribution

#### Abstract

In this article, by making use of a $q$-analogue of

the familiar Borel distribution, we introduce

two new subclasses:

$$\mathcal{S}_{\rm starlike}^{\alpha,\lambda,q}(b,A,B)

\qquad \text{and} \qquad

\mathcal{S}_{\rm convex}^{\alpha,\lambda,q}(b,A,B)$$

of starlike and convex functions in the open unit disk $\Delta$

with respect to symmetric and conjugate points. We obtain

some properties including the Taylor-Maclaurin coefficient

estimates for functions in each of these subclasses and

deduce various corollaries and consequences

of the main results. We also

indicate relevant connections of each of these subclasses

$\;\mathcal{S}_{\rm starlike}^{\alpha,\lambda,q}(b,A,B)\;$

and $\;\mathcal{S}_{\rm convex}^{\alpha,\lambda,q}(b,A,B)\;$

with the function classes which were investigated in several

earlier works.

### Refbacks

- There are currently no refbacks.