On a new class of analytic functions associated with conic domain

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk EE onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.

► We generalized the conic domain and defined a new class of analytic functions.
► We made correction in selecting the range interval of order of conic domain.
► We gave a sufficient condition for the class of generalized kk-starlike functions.
► We determined the radius of generalized kk-uniform convexity of univalent functions.
► An integral preserving property of generalized kk-starlike functions is also shown.