锥上的逼近定理和不动点定理

APPROXIMATION THEOREMS AND FIXED POINT THEOREMS IN CONES

设E是实Frechet空间,K是E上的锥,D是含θ点的开凸集,记DK=D(?)K,设映射T:(?)_k(?)E→2~k是连续凝聚映射,则存在u(?)使P(T(u)—u)=P(T(u)—(?)),其中P是集D的Minkowski泛函,作为本定理的应用,给出了一些新的不动点定理,同时,在适当条件下,本文给出了锥上的环上的一个逼近定理。

This paper investigates the validity of an intesting approximation theorem of Fan [1.Theorem 2] in cones, and proves that it is true for a continuous condensing multifunction defined on the closure of a open convex set in cones and that it is true on an annulus ff suitable inner boundary conditions are satisfied, as applications of the theorem, some new fixed point theorems are derived, the results are extensions of theorems of T. C. Lin [1].