TANG Li-ping, YANG Xin-min. A Note on Some New Characteristics of D-Semi-Preinvexity[J]. Applied Mathematics and Mechanics, 2015, 36(3): 325-331. doi: 10.3879/j.issn.1000-0887.2015.03.010
Citation: TANG Li-ping, YANG Xin-min. A Note on Some New Characteristics of D-Semi-Preinvexity[J]. Applied Mathematics and Mechanics, 2015, 36(3): 325-331. doi: 10.3879/j.issn.1000-0887.2015.03.010

A Note on Some New Characteristics of D-Semi-Preinvexity

doi: 10.3879/j.issn.1000-0887.2015.03.010
Funds:  The National Natural Science Foundation of China(Key Program)(11431004);The National Natural Science Foundation of China(11271391)
  • Received Date: 2014-12-09
  • Rev Recd Date: 2014-12-24
  • Publish Date: 2015-03-15
  • Some new properties of semi-preinvexity in the sense of cones were studied. Firstly, Example 4 in the paper of PENG Zai-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-semi-prequasiinvexity.
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