关于序Banach空间中拟半可导凝聚映象的不动点定理

FIXED POINT THEOREMS FOR QUASI-SEMIDIFFERENTIABLE CONDENSING MAPPING IN ORDERED BANACH SPACE

M.A.Krasnoselskii在1964年讨论了在θ点,或在∞点存在Fréchet导数的全连续算子的不动点的情况,H.Amann 在1976年将这些结果推广到在θ点或在∞点存在Fréchet 导数的K-集压缩映象,W.V.Petryshyn 在1988年引进了半可导的概述,将这些结果推广到在θ点或在∞点存在半导数的K-集压缩映象.本文改进了W.V.Petryshyn 的证明方法,将这些结果推广到更广泛的拟半可导凝聚映象.

The purpose of this paper is to extend some fixed point theorems of Krasnoselskii for completely continuous,ofAmann for strict set-contractions,which are Frechet differentiable at θ and/or at ∞,and of Petryshyn for strict set-con-tractions,which are semidifferentiable at θ and/or at ∞ to those which are quasi-semidifferentiable condensing map-pings.