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The authors propose to investigate some new criteria for a certain class of meromorphically strongly starlike functions in the punctured open unit disk. Some intriguing applications that arise as special cases of the main results, which are presented in this study, are also considered.

In the present paper, we investigated some conditions to be in the class of Carathéodory functions by using the concept of the first-order differential subordinations. Moreover, various interesting special cases were considered in the geometric function theory as applications of main results presented here. [ABSTRACT FROM AUTHOR]

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and α -exponentially bi-convex functions involving functions with bounded boundary rotation of order ν. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete–Szegö coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature. [ABSTRACT FROM AUTHOR]