An Inequality for Algebroid Functions and Some Applications

Abstract

In this paper we present a version for algebroid functions of an inequality due to Barsegian (Math URSS Sbornik 42(2):155, 1982) and we get two consequences: first a kind of deficiency relation for curves (preimages of an algebroid function, the so-called $$\Gamma $$ -lines) which is an extension of the well-known relation of Barsegian ( $$\Gamma $$ -lines. On the geometry of real and complex functions. Taylor & Francis, London, 2002) and secondly a proximity principle for the preimages of an algebroid function, also an extension of the principle for meromorphic functions.