LOCALLY AFFINE FUNCTIONS

The Monge-Ampère equation and related boundary value problem are a source example for the non-linear potential theory, and for convex analysis ([1-5, 8]). Moreover the concept of the locally convex function is introduced in the study of the solutions of this equations ([1, 3, 5, 9]). In this paper an attempt is made to define a generalization of this type of functions (i.e. it is defined the quasi-locally convex functions), some properties of the quasi-locally convex functions are studied, and an important example of quasi-locally affine function is presented.