一类混合单调算子的不动点的存在唯一性

Existence and Uniqueness of Fixed Points of a Class of Mixed Monotone Operators

中文关键词:  锥与半序  φ凹-（-ψ）凸算子  混合单调算子  Guo凸算子  不动点

英文关键词:cone and semiorder  φ-concave-（-ψ）-convex operator  mixed monotone operator  Guo-convex operator  fixed point

中文摘要:

      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,在非紧非连续条件下,得到了算子的不动点的存在唯一性和迭代收敛性,进而得到了具有a凹-Guo凸,凹-Guo凸,μ₀凹-凸,μ₀凹-(-a)凸或α₁凹-(-α₂)凸等性质的混合单调算子的新不动点定理。

英文摘要:

      In this paper, the definition of φ-concave-(ψ-)-convex operator is introduced, and a class of mixed monotone operators with certain concavity and convexity properties arc dis- cussed. Without any compactness or continuity of the operators , the existence and unique- ness for the fixed point of the operators is obtained. As corollaries, some new results about these operators are produced.