In this chapter , a class of mixed monotone operators with a - t type convexity and concavity has been discussed through cone theory and by using the method of lower - upper solutions , the skill of monotone iterative . the sufficient and necessary conditions for existence and uniqueness of their fixed points are given . the results in relevant literatures are generalized or included . these sufficient and necessary conditions are out of the limitation of only giving the sufficient conditions in previous papers , and improve the relevant results essentially ; for a class of mixed monotone operators with general a - t type convexity and concavity , the sufficient and necessary conditions for existence and uniqueness of their fixed points are given by introducing the concept of ? adjoint sequence " . for a class of sublinear mixed monotone operators , the sufficient and necessary conditions for existence and uniqueness of their fixed points are also given by using diagonal process with double - lower ordinate arrangement . and a cl ass of mixed monotone operators with ( a , / 3 ) type convexity and concavity is also studied through some proper transforms , the sufficient and necessary conditions for existence and uniqueness of their fixed points are also given under certain conditions 通過(guò)運(yùn)用錐理論,采用上下解方法、單調(diào)迭代技巧等討論了一類? t型凹凸的混合單調(diào)算子,給出了其存在唯一不動(dòng)點(diǎn)的充分必要條件,含蓋了相關(guān)文獻(xiàn)的部分工作,所給的充要條件彌補(bǔ)了以往只給出充分條件的局限性,對(duì)文獻(xiàn)中的相關(guān)工作做了本質(zhì)性的改進(jìn);對(duì)于廣義? t型凹凸混合單調(diào)算子,通過(guò)引入“伴隨列”的概念,也給出了其存在唯一不動(dòng)點(diǎn)的充分必要條件;對(duì)于次線性混合單調(diào)算子,通過(guò)運(yùn)用雙下標(biāo)排列的對(duì)角線方法,也給出了其存在唯一不動(dòng)點(diǎn)的充分必要條件;通過(guò)適當(dāng)?shù)淖儞Q技巧,討論了( , )型凹凸混合單調(diào)算子,在一定的條件下,給出了其存在唯一不動(dòng)點(diǎn)的充分必要條件。