  This paper is concerned with the qualitative properties of viscocity
solutions to a class of Hamilton-Jacobi equations (HJEs) in Banach spaces.
Specifically, based on the concept of $\beta$-derivative \cite{DGZ93b} we
establish the existence, uniqueness and stability of $\beta$-viscosity
solutions for a class of HJEs in the form $u+H(x,u,Du)=0.$ The obtained results
in this paper extend ealier works in the literature, for example, \cite{CL85},
\cite{CL86} and \cite{DGZ93b}.
