Banach空间中的广义E-单调性

On Generalized E-Monotonicity in Banach Spaces

中文关键词:  $E$-预内凸性  $E$-内凸性  不变$E$-单调性  关系.

英文关键词:$E$-preinvexity  $E$-invexity  invariant $E$-monotonicity  relations.

中文摘要:

      本文在Banach空间中定义了几种新的广义$E$-凸性和广义$E$-单调性.讨论了$E$-预内凸, $E$-拟预内凸 (伪,拟)$E$-内凸和不变$E$-单调性之间的关系,这些关系是一些已有结果的推广.

英文摘要:

      Several new kinds of generalized $E$-preinvexity and generalized invariant $E$-monotonicity are introduced in the setting of Banach spaces. The relations between $E$-preinvexity, $E$-prequasiinvexity, (pseudo, quasi) $E$-invexity and invariant (pseudo, quasi) $E$-monotonicity are studied, which can be viewed as an extension of some known results.