Acta Universitatis Apulensis ISSN: 1582-5329 http://www.uab.ro/auajournal/ No. 44/2015 pp. 1-8 doi: 10.17114/j.aua.2015.44.01 MOCANU AND S ¸ERB TYPE UNIVALENCE CRITERIA FOR SOME GENERAL INTEGRAL OPERATORS V. Pescar and N. Breaz Abstract. In this paper we derive univalence criteria for two general integral operators defined by analytic functions in the open unit disk, using the univalence criteria given by Pascu, respectively a lemma given by Mocanu and S ¸erb. 2010 Mathematics Subject Classification : 30C45. Keywords: analytic functions, integral operators, univalence. 1. Introduction Let A be the class of functions f of the form f (z )= z + ∞  n=2 a n z n , normalized by f (0) = f ′ (0) − 1 = 0, which are analytic in the open unit disk, U = {z ∈ C : |z | < 1}. We denote S the subclass of A consisting of functions which are univalent in U . One of the topics in geometric function theory is the study of univalence of the integral operators. In the last decade, some general integral operators, defined as a family of integral operators, using more than one analytic function in their definition, have been studied with respect to their univalence (see for example, the works [2], [3] and [16], and many other recent paper as [5], [8], [19]). In this paper, the univalence study is focused on the following general integral operators: T n (z )=    β z  0 u β−1 ( f ′ 1 (u) ) γ 1 ... ( f ′ n (u) ) γn du    1 β , (1) 1