ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS

Title & Authors
ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS
An, Jong-Su;

Abstract
In this paper, it is shown that if f satisfies the following functional inequality (0.1) $\small{{\parallel}\sum\limits_{i,j=1}^3\;f{(xi,yj)}{\parallel}{\leq}{\parallel}f(x_1+x_2+x_3,\;y_1+y_2+y_3){\parallel}}$ then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) $\small{{\parallel}2\sum\limits_{j=1}^3\;f{(x_j,\;z)}+2\sum\limits_{j=1}^3\;f{(x_j,\;w)-f(\sum\limits_{j=1}^3\;xj,\;z-w)}{\parallel}{\leq}f(\sum\limits_{j=1}^3\;xj,\;z+w){\parallel}}$ then f is an additive-quadratic mapping.
Keywords
Language
English
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