Many classical univalence criteria depending on the Schwarzian derivative are special cases of a result, proved in [18], involving both conformal mappings and conformal metrics. The classical theorems for analytic functions on the disk emerge by choosing appropriate conformal metrics and computing a generalized Schwarzian. The results in this paper address questions of extending functions which...

"The error function takes place in a wide range the elds of mathe- matics, mathematical physics and natural sciences. The aim current paper is to investigate certain properties such as univalence close-to-convexity normalized imaginary function, which its region symmetric with respect real axis. Some other outcomes are also obtained."

In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution this equation real kernel ?-harmonic mappings. paper, we study some geometric properties give univalence criteria and sufficient coefficient conditions for mappings that are fully starlike or convex ?, ? [0, 1). Furthermore, establish Landau type theorem