On Certain Classes of Convex Functions

Abstract EN

For real numbers α and β such that 0≤α<1<β, we denote by ?α,β the class of normalized analytic functions which satisfy the following two sided-inequality: α<ℜ1+zf′′z/f′z<β z∈?, where ? denotes the open unit disk.

We find some relationships involving functions in the class ?(α,β).

And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class.

Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.