Abstract
<abstract><p>The objective of the current examination is to present new sub-classes of $ q $-convex and $ q $-starlike functions inside $ \mathcal E = \left\{z\in\mathbb C: \left|z\right| &lt; 1\right\} $, by $ q $-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and $ q $-limits on real part.</p></abstract>
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