1) Semistrictly Quasimonotonicity
半严格拟单调
2) semistrict invariant quasimonotone map
半严格不变拟单调映射
3) Strictly Quasimonotonicity
严格拟单调
4) strictly invariant quasimonotone
严格不变拟单调
1.
In this paper, the strictly invariant quasimonotone is defined as an extension of strictly quasimonotone: Let K of R~n be an invex set with respect to η:R~n×R~n→R~n.
本文对严格拟单调进行推广,定义了严格不变拟单调:设K为Rn中的不变凸集,η:Rn×Rn→Rn,如果f是不变拟单调的,且对x,y∈K,x≠y,存在z∈{y+λη(x,y):λ∈(0,1)},使得η(x,y)Tf(z)≠0,则称f为集合K上相对于η的严格不变拟单调映射。
5) Strictly Monotone
严格单调
1.
Let f(x), g(x) be strictly monotone and integrable, p(x), q(x) be always positive and integrable over the same interval [a, b], according to mean value theorem for integrals, there is sole mean value ξ f,p (a,b) and ξ g,q (a,b) respectively.
设f (x)、g(x)在同一区间[a,b]内严格单调并可积,p(x)、q(x)恒正可积,按积分中值定理各有唯一的中间点ξf ,p(a,b)和ξg,q(a,b) 。
2.
In this paper, under the condition of strictly monotone, discusses str ictly monotone , continuity and derivatiability of integral mean value function, and the general results are obtained.
本文在严格单调的前提下 ,讨论了积分中值函数的严格单调性、连续性和可微性 ,得到了具有一般性的结论。
3.
This paper,under the condition of strictly monotone,discusses strictly monotone increasingproperty,continuity and differentiability of integral mean value function ξ(x),and weakens the condi-tion used in the document [1].
本文在严格单调的前提下，讨论了积分中值函数ξ(x)的严格递增性、连续性和可微性，减弱了文[1]所使用的条件。
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