The F-inclusion property and F-convexity in normed spaces

In this paper, the F-inclusion property of nonempty subsets in normed spaces is introduced. By applying this concept, two sufficient conditions for F-convex sets are obtained which generalize the corresponding result from [E.A. Youness, E-convex sets, E-convex functions, and E-convex programming, J. Optim. Theory Appl. 102 (1999) 439-450].