半局部η-伪线性函数的一些性质

Some Characterizations of Semilocal η-Pseudolinear Functions

作为半局部伪线性函数和η-伪线性函数的推广,本文利用半可微性提出了一类新的广义凸性函数—半局部η-伪线性函数。同时,本文建立了f在Γ上是半局部η-伪线性的当且仅当存在p:Γ×Γ→R,满足p(x,y)>0,x,y∈Γ,f(y)=f(x)+p(x,y)df+(x,η(y,x))等性质。本文的结果是对文献[2]和[4]中相应结果的改进与推广。

As a generalization of the semilocally pseudolinear functions and η-pseudolinear functions,we proposed a new class of generalized convexity—the semilocally η-pseudolinear functions.Also,we established some properties including that f is semilocally η-pseudolinear if and only if there exists a function p:Γ×Γ→R such that p(x,y)>0 and x,y∈Γ,f(y)=f(x)+p(x,y)df+(x,η(y,x)).Our results improved and extended the results in references [2] and [4].