A Criterion for Univalent Meromorphic Functions

Let D = {z is an element of C, vertical bar z vertical bar < 1} and A(p) be the set of meromorphic functions in D possessing only simple pole at the point p with p is an element of (0, 1). The aim of this paper is to give a criterion by mean of conditions on the parameters alpha, beta is an element of C, lambda > 0 and g is an element of A(p) for functions in the class denoted P-alpha,P-beta;h(p; lambda) of functions f is an element of A(p) satisfying a differential Inequality of the form vertical bar alpha (z/f(z))'' + beta(z/g(z))'' vertical bar <= lambda mu, z is an element of D to be univalent in the disc D, where mu = (1 - p/1 + p)(2).