Construction and determination of univalent biharmonic mappings

Abstract

We construct a family of biharmonic mappings $W_{\alpha ,\beta }$, which arises from analytic functions and has two parameters. Some sufficient conditions for $W_{\alpha ,\beta }$ to be sense-preserving and univalent are explored. The radii of full convexity and starlikeness of $W_{\alpha ,\beta }$ are determined. Some sufficient conditions for biharmonic mappings to be fully starlike and fully convex are obtained. Many related previous results are generalized.