Abstract
Abstract The article studies a new class of analytic functions whose set of values is contained in an angular domain with curved sides with a vertex at the origin of the coordinate system. In particular, the set of values of the functions under study can be contained in domains bounded by the right loop of the generalized Bernoulli lemniscate, as well as in domains in the form of a circle, angle, or half-plane. In this class, estimates of the modulus of the function and the modulus of the logarithmic derivative of the function are obtained. As an example of the application of these estimates, growth theorems and radii of starlikeness of some classes of close-to-starlike and doubly close-to-starlike functions are obtained. All results of the article are exact. In special cases, previously known results are obtained.