Abstract
A significant generalization of convexity is constituted by the concept of E-convexity, and our aim in this paper is to define a new class of functions depending on E-convexity, called logarithmic E -convex functions and to discuss their properties. Logarithmic E -convex functions are extended to lo-garithmic quasi E-convex and logarithmic pseudo E-convex functions and some results concerning them are presented. Logarithmic E -convex multi-objective programming problem is formulated. Finally, the sufficient and necessary conditions for a feasible solution to be an efficient solution for multi-objective programming problem involving logarithmic E -convex functions are derived.