中文摘要：

研究了锥意义下的半预不变凸性的新性质.首先,对彭再云等的文献（彭再云,李科科,唐平,黄应全.向量值D-半预不变真拟凸映射的判定与性质[J].重庆师范大学学报（自然科学版）,2014,31（5）：18-25.）中的例4进行了修正,使其满足条件E.然后,给出了条件E1的一个重要性质,并在此基础上结合稠密性结果,分别利用D-半严格半预不变真拟凸性和D-严格半预不变真拟凸性建立了D-半预不变凸性的刻画.最后利用D-半预不变真拟凸性给出了D-半预不变凸性的刻画.

英文摘要：

Some new properties of semi-preinvexity in the sense of cones were studied. Firstly,Example4 in the paper of PENG Z ai-yun,etc.（ PENG Zai-yun,LI Ke-ke,TANG Ping,HUANG Ying-quan.Characterizations and criterions of D-semiprequasi-invex mappings[J]. Journal of Chongqing Normal University（ Natural Science）,2014,31（ 5） ： 18-25.） was modified to satisfy condition E. Then,an important property of condition E1 was obtained. Based on this property and the results of density,two characterizations of D-semi-preinvexity were established by means of D-semi-strict semi-prequasiinvexity and D-strict semi-prequasiinvexity,respectivley. In the end, D-semi-preinvexity was characterized with D-semiprequasiinvexity.