In this paper, we investigate a von Karman plate system with general type of relaxation functions on the boundary. We derive the general decay rate result without requiring the assumption that the initial value $w_0\equiv 0$ on the boundary, using the multiplier method and some properties of the convex functions. Here we consider the resolvent kernels $k_i(i=1,2)$, namely $k_i^{″}(t)\ge -{\xi }_i(t)G_i(-k_i^{\prime }(t))$, where $G_i$ are convex and increasing functions near the origin and ${\xi }_i$ are positive nonincreasing functions. Moreover, the energy decay rates depend on the functions ${\xi }_i$ and $G_i.$ These general decay estimates allow for certain relaxation functions which are not necessarily of exponential or polynomial decay and therefore improve earlier results in the literature.