Abstract
A new class of meromorphic functions f that are univalent in the punctured unit disk U* = {z : 0 < vertical bar z vertical bar < 1} is introduced. This class is denoted by MU and consisting of functions f defined by vertical bar 1 + f(1)(z)/f(2)(z)vertical bar < 1 and zf(z) not equal 0, whenever z is an element of U = {z : vertical bar z vertical bar < 1}. For every n >= 2, sharp bound for the nth derivative of 1/(zf(z)) that implies univalency of f in U* is established. In particular, the best improvements for known univalence criteria are obtained. Distortion and growth estimates are investigated. Further, various sufficient coefficient conditions and a necessary coefficient condition for f to be in MU are derived and best radii of univalence are obtained for certain cases.