In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

This paper aims to introduce a measure of the non-univalency harmonic mapping. By using it, we find best approximation an analytic function by univalent

Refinements and generalizations of the classical variational principles of conformal mappings are presented; mainly, they follow from potential theory and symmetrization. Part of the results can be viewed as properties of Robin functions and Robin capacities, and also as distortion theorems for univalent functions in finitely connected domains. §