Characterizations of D-Properly Semi-Prequasi-Invex Mappings
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摘要: 研究了D-半预不变真拟凸映射的性质.首先,举例验证了满足条件E的η是大量存在的.然后,说明了D-半预不变真拟凸映射的水平集是半不变凸集,并运用D-上半连续性、*-上半连续性和中间点的D-半预不变真拟凸性,给出了D-半预不变真拟凸映射的两个等价刻画.最后,在中间点D-严格半预不变真拟凸性条件下,建立了D-半严格半预不变真拟凸映射和D-严格半预不变真拟凸映射的等价关系.
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关键词:
- D-半预不变真拟凸映射 /
- 半不变凸集 /
- 条件E
Abstract: The properties of D-properly semi-prequasi-invex mappings were studied. Firstly, it was verified that the η values satisfying condition E exist massively. Secondly, the level set of theD-properly semi-prequasi-invex mapping was proved to be a semi-invex set, and two equivalent propositions of the D-properly semi-prequasi-invex mapping were given with D-upper semi-continuity, *-upper semi-continuity and intermediate-point D-properly semi-prequasi-invexity. Finally, the equivalent relation between the D-properly semi-strict semi-prequasi-invex mapping and the D-properly strict semi-prequasi-invex mapping was established under the condition of the intermediate-point D-properly strict semi-prequasi-invexity.-
Key words:
- D-properly semi-prequasi-invex mapping /
- semi-invex set /
- condition E
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