Some Properties of (F-K)-Convex Mapping in Vector Spaces

Optimization theory is the most important part of the optimization as well as an important theoretical basis in operational research. Convex set and convex mapping, as basic theoretical results in optimization theory, are applied in many fields of mathematics. Accordingly, development of the convexity of sets and functions has practical significance. In 1999 Youness first introduced the concept of E-convex set and E-convex function, then Yang and Chen defined the semi-E-convex function and listed its properties, In recent decades, set-valued analysis and convex analysis, as the tools of researching the optimized theorem, have made great progress, as well as provides new ideas, new methods for the generalized convexity study, and many useful conclusions, which also contributed to develop generalized convexity to be a focus for domestic and foreign scholars. In this paper, we introduce (F, K) -- convex set, (F, K) -- convex mapping and semi (F, K) -- convex mapping in vector spaces, and some properties of these concepts are given.