In the current paper, we study a majorization issue for a general category ${\mathcal{S}}^{*}\left(\vartheta \right)$ of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions $\vartheta$ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.

In the present paper, we consider various subclasses of star-like functions, which are defined by subordination and then we obtain several subordination implications related to these subclasses. Some coefficient bounds for functions belonging to some subclasses of star-like functions are also estimated. Moreover, we give some related connections of the outcomes stated here with those obtained earlier.

The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order $\alpha$ and strongly close-to-convexity of order $\alpha$ . Furthermore, the main results presented here are compared with the previous outcomes obtained in this area.