Properties of a generalized class of analytic functions with coefficient inequality.

Let (β_n)n≥2 be a sequence of nonnegative real numbers and δ be a positive real number. We introduce the subclass A(β_n, δ) of analytic functions, with the property that the Taylor coefficients of the function f satisfies Σ^∞_n≥2β_n︱a_n︱≤ δ, where f(z) = z + Σ^∞_n=2 a_nzⁿ . The class A(β_n, δ) contains nonunivalent functions for some choices of (β_n)_n≥2 . In this paper, we provide some general properties of functions belonging to the class A(β_n, δ), such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. Applying our results, we recover some known results on subclasses related to coefficient inequality. Some applications to starlike and convex functions of order α are also mentioned. [ABSTRACT FROM AUTHOR]