B P International

In paper [1], Petru T. Mocanu has obtained sufficient conditions for a function in the classes C 1 (U), respectively C 2 (U) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively convex. Those conditions are similar to those in the analytic case. In paper [2], Petru T. Mocanu has obtained sufficient conditions of univalency for complex functions in the class C 1 which are also similar to those in the analytic case. Having those papers as inspiration, we have tried to introduce the notion of subordination for non-analytic functions of classes C 1 and C 2 following the classical theory of differential subordination for analytic functions introduced by S.S. Miller and P.T. Mocanu in papers [3] and [4] and developed in the book [5]. Let Ω be any set in the complex plane C, let p be a non-analytic function in the unit disc U, p ∈ C 2 (U) and let ψ(r, s, t; z) : C 3 ×U → C. In article [6] we have considered the problem of determining propertie...