关于赋范线性空间中的三类泛函方程  

On the Three Kinds of Functional Equation of in the Normed Linear Spaces

作　　者：姚云飞[1] 

机构地区：[1]阜阳师范学院数学系,安徽阜阳236032

出　　处：《工科数学》2002年第5期49-53,共5页Journal of Mathematics For Technology

摘　　要：在赋范线性空间中考察下列几类泛函方程( ) f(x) g(y) =h(x+y) ,　 ( ) f(x+y) =f(x) f(y) ,　 ( ) f(x+y) =f(x) +f(y) +ag(x) g(y)的性质与解以及彼此之间的关系 .This paper deals with the properties. Solution and their each other reations of the following functional equation (Ⅰ) f(x)g(y)=h(x+y), (Ⅱ) f(x+y)=f(x)f(y), (Ⅲ) f(x+y)=f(x)+f(y)+ag(x)g(y) of in the normed linear spaces.

关 键 词：泛函方程 赋范线性空间 凸泛函 共轭空间 连续泛函 

分 类 号：O177.91[理学—数学]