ON SOME CLASSES OF DOUBLY NEARLY CONVEX FUNCTIONS

 Based on the results obtained by the authors in one of the previous articles (Bulletin of the Kazakh-British Technical University, 2024, 21(2), pp.127-138), the class of doubly close-to-convex in the unit disk
of the functions f(z), set using the conditions 

 where the functions f(z), g(z) and h(z) have expansions of the form 

, and the function h(z) is convex. In this class, the theorems of distortion, rotation and radius of convexity are established. In particular cases, we obtain both a number of previously known and a number of new original results for doubly close-to-convex and close-to-convex functions. Based on this class, a class of doubly close-to-starlike functions is introduced, for which the growth theorem and the star radius are found. For specific values of the parameters previously known results for close-to-starlike functions are obtained.

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