提出了一类新的向量值映射-$D$-$E$-预不变真拟凸映射, 它是$E$-预不变凸映射(Fulga和Preda, 2009) 与 $D$-预不变真拟凸映射(彭建文, 2003)的真推广. 首先, 用 例子说明$E$-不变凸集, $D$-$E$-预不变真拟凸映射的存在性; 然后, 讨论$D$-$E$-预不变真拟凸映射的性质, 并获 得$D$-$E$-半严格预不变真拟凸映射在向量优化问题中的 一个重要应用; 最后, 对$D$-$E$-半严格预不变 真拟凸与$D$-$E$-预不变真拟凸映射之间的关系做 了探究, 并举例验证了所得结果.

A class of new vector-valued generalized convex mapping-$D$-$E$-properly prequsai-invex mapping, which is a true generalization of $E$-preinvex mapping (Fulga and Preda, 2009) and $D$-properly prequasi-invex mapping (Peng, 2003), is discussed in this paper. Firstly, examples are given to show the existence of $E$-invex sets and $D$-$E$-properly prequasi-invex mappings. Secondly, characterizations of $D$-$E$-properly prequsai-invex mappings and an important application of $D$-$E$-properly semistrictly prequasi-invexity in vector optimization are obtained. Finally, relationships between $D$-$E$-properly semistrictly prequasi-invexity and $D$-$E$-properly prequasi-invexity are discussed, then some examples are given to illustrate the obtained results.