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

Research Article Functional Inequalities Associated with Jordan-von Neumann-Type Additive Functional Equations

Ulam [1] gave a talk before theMathematics Club of the University ofWisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G with metric ρ( , ). Given > 0, does there exist a δ > 0 such that if f :G G satisfies ρ( f (xy), f (x) f (y)) < δ for all x, y G, then a hom...

Functional Emergence with Multiple von Neumann Computers

For the spontaneous emergence of the function in the multiagent system through evolution, a designer (man) must refrain from designing agents to excess and make agents behave as freely as possible based upon the rules within themselves. All the designer can do is to implement the system architecture and to specify the environments. The von Neumann machine, which is logically equivalent to the u...

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

On Functional Inequalities Originating from Module Jordan Left Derivations

Von Neumann Betti Numbers and Novikov Type Inequalities

In this paper we show that Novikov type inequalities for closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a consequence we obtain a vanishing theorem for L cohomology. We also prove that von Neumann Betti numbers coincide with the Novikov numbers for free abelian coverings. §0. Introduction S. Novikov and M. Shubin [NS] proved that Morse inequalities for ...