  The curvature estimates of quotient curvature equation do not always exist
even for convex setting \cite{GRW}. Thus it is natural question to find other
type of elliptic equations possessing curvature estimates. In this paper, we
discuss the existence of curvature estimate for fully nonlinear elliptic
equations defined by symmetric polynomials, mainlly, the linear combination of
elementary symmetric polynomials.
