On k-uniformly starlike convex functions associated with (j, m)-ply symmetric points

In this paper, we aim to discuss several results associated with conical domains and some general properties. By utilizing some conical sections, we introduce a new class of analytic functions with respect to (j, m)-ply symmetric points, \(j=0,1,\ldots ,m-1\) and \(m \in \mathbb {N}\). Also, we formulate certain k-uniformly convex starlike functions influenced by the principle of the differential subordinations. In addition, we derive coefficient bounds for various functions in the given classes of analytic functions and evaluate certain sufficiency criteria in a form of convolutions. Over and above, we derive interesting results involving starlike functions as well.