φ凹(-Ψ)凸混合单调算子不动点存在惟一性及其应用

Existence and Uniqueness for the Fixed Points of φ Concave-(-ψ) Convex Mixed Monotone Operators and Its Applications

该文引入了φ凹-(—ψ)凸算子,统一处理了一类具有某种凹凸性的混合单调算子,在非紧非连续的条件下,利用单凋叠代技巧证明了不动点的存在惟一,进而得到了具有α凹-凸、凹-(—α)凸、α凹-Guo凸、凹-Guo凸、e凹-Guo凸、e凹-凸、e凹-(—α)凸以及α_1凹-(—α_2)凸等性质的混合单调算子的新不动点定理,并将所获结果应用于Hammerstein非线性积分方程。

In this paper, the definition of ФConcave-（-φ） convex operator is introduced and a class of mixed monotone operators are discussed. Without any compactness or continuity of the operators, the existence and uniqueness for the fixed points of the operators with such concavity and convexity, as α concavity-convexity, concavity-（-α） convexity, α concavity-Guo convexity, concavity-Guo convexity, e concavity-Guo convexity, e concavity-convexity, e concavity-（-α） convexity and α1 concavity-（-α2） convexity, is obtained. As corollaries, some new results about these operators are produced. In the end, the new results are applied to the Hammerstein integral equations on unbounded regions.