PENG Zai-yun, WANG Kun-ying, ZHAO Yong, ZHANG Shi-sheng. Characterizations and Applications of D-η-Semipreinvex Mappings[J]. Applied Mathematics and Mechanics, 2014, 35(2): 202-211. doi: 10.3879/j.issn.1000-0887.2014.02.008
Citation: PENG Zai-yun, WANG Kun-ying, ZHAO Yong, ZHANG Shi-sheng. Characterizations and Applications of D-η-Semipreinvex Mappings[J]. Applied Mathematics and Mechanics, 2014, 35(2): 202-211. doi: 10.3879/j.issn.1000-0887.2014.02.008

Characterizations and Applications of D-η-Semipreinvex Mappings

doi: 10.3879/j.issn.1000-0887.2014.02.008
Funds:  The National Natural Science Foundation of China(11271389; 11301571)
  • Received Date: 2013-07-16
  • Publish Date: 2014-02-15
  • A class of new vector valued generalized convex mappings—D-η-semipreinvex mappings, which was a true generalization of D-preinvex mapping, was given. Firstly, examples were given to show the existence of D-η-semipreinvexmappings and illustrate the differences between D-η-semistrictly semi-preinvex and D-η-semipreinv exmapping. Secondly, a criterion of D-η-semipreinv exity was given, and the relationships among D-η-semipreinvexity, D-η-strict semipreinvexity and D-η-semistrict semipreinvexity were discussed. Finally, an important application of D-η-semistrict semipreinvexity in vector optimization was discussed, then give an example was given to illustrate the result.
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