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In this paper, we introduce and investigate new classes of normalized analytic functions in an open unit disk with bounded radius and bounded boundary rotation by using the subordination. We discuss inclusion results, co-efficient bounds, growth and distortion theorems of the classes. Moreover, we compute the radii of strong starlikeness, convexity and starlikeness of the classes. It is interesting to mention that most of our findings are best possible as compared to the existing results in the literature.

On strongly starlike and strongly convex functions with bounded radius and bounded boundary rotation