m—增生算子的G—可微性和取零值点

这篇文章讨论有关m—增生算子的两个问题。一个是m—增生算子 A 和它的 G—可微性间的关系,我们利用 Caristi 不动点定理得出了如下结果:A 是具有凸定义域的闭G—可微算子,若 dAx 对每一 x∈(DA)是m—增生的,则 A 是 m—增生算子。另一方面,我们还讨论了m—增生算子的取零值问题,改进了[5]中的几个定理,去掉了要求非扩张映象在每一有界闭凸集上具有不动点性质这一较难验证的条件。

G-differentiable and Zeros of m-accretive Operators

In this paper we deal with two problems of m-accretive operators. First, we discuss the relation between m-accretive A and G-differentiable. Applying the fixed point Caristi's theorem we get the following results. Let A be a closed Gateaux differentiable operator with a convex domain. If dAxis m-accretive for each x D(A), then A is also m-accretive. Second, also we discuss the zeros of m-accretive operators. A few theorems in [5] are improved. In the theorems we remove more difficult conditions for the verificatiou, which is that each bounded closed convex subset has fixed point property for nonexpansive self-mapping.