Abstract: Firstly, a class of pseudo-E-convex functions without differentiability condition is defined in this paper, which is a proper generalization of E-convex functions and pseudoconvex functions without differentiability condition. The existence of such functions is verified with an example. Furthermore, the relationships between pseudo-E- convex functions and other functions are discussed. These indicate that pseudo-E-convex functions without differentiability condition are more general and have a wider range of applications. Secondly, some properties of pseudo-E-convex functions are obtained. Finally, in terms of optimality, the relationship between the fixed points of the mapping E and their global optimal solutions is discussed for the pseudo-E-convex programming problems ($\mathrm{P}$) and ($\mathrm{P}_{E}$), the local-global property of the optimal solutions and the uniqueness of the global optimal solution for programming problem ($\mathrm{P}$) are obtained, and the examples are provided to verify the results respectively.

Key words: (strictly) pseudo-E-convex functions, pseudo-E-convex programming, optimal solutions