the chapter is devoted to the existence and uniqueness of fixed point of monotone operators with concavity or convexity . in 2.1 . we present some relations : among the various concave operators, among the various-convex operators 在本节中,我们也讨论了具有序凹(凸)性的单调算子及具有u_o凹凸性的混合单调算子唯一正不动点的存在性问题。