In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

In this paper, we study some new results such as coefficients bounds and Fekete–Szegö inequalities of the certain classes starlike and convex functions associated with shell-like defined using the concept of Ruscheweyh [Formula: see text]-differential operator. Comparisons of new results with those that were obtained in earlier investigation are given as corollaries.

We introduce and we study certain classes of analytic functions which are defined by making use of the q-derivative operator. Coefficient inequalities for functions in these classes are discussed. Some interesting consequences of the results are also pointed out.