CLASSES OF CLOSE-TO-STARLIKE FUNCTIONS BASED ON THE REFERENCE FUNCTION OF A GENERAL FORM

Abstract

The purpose of the article is to introduce and explore a wide class of doubly close-to-starlike functions, while demonstrating a unified approach to solving a certain range of extreme problems. The article defines a reference function of a general form – a starlike function, on the basis of which classes of close-to-starlike and doubly close-to-starlike functions can be constructed. On the basis of a general support function containing three parameters and new estimates of analytical functions, a generalization of various classes of close-to-starlike and doubly close-to-starlike functions is introduced, considered in a number of articles published in recent years, including the introduced class contains a generalized class of typically real functions. The properties of the introduced class of functions are studied, for example, the growth theorem, estimates of the modulus of the logarithmic derivative of the function and the radius of starlikeness are obtained, in particular cases leading to previously known results and representing new results. All the results of the article are accurate.

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