Banach空间中具有Pr-紧性随机算子方程

RANDOM EQUATIONS INVOLVING Pr-COMPACT OPERATORS IN BANACH SPACE

本文主要研究了具有 Pr-紧性随机算子方程的随机解的存在性问题。主要结果是将〔2〕中的有关 Pr-紧算子方程的主要定理做了随机化处理。作为推论,我们得到了〔3〕中的主要结果以及 Schauder;Rothe;Altman;Tychonoff 和更为一般的 Krasnoselsky 型随机不动点定理。利用所得结果;我们还证明了一个存在性定理。

In this paper the existence of random solutions of operators equationsinvolving Pr-compact operators is studied.The random analog of a deter-ministic result obtained by Petryshyn [2] for such operators is the maintheorem.As corollaries,we get the main theorem in [3] and Schauder's,Rothe's,Altman's,Tychonoff's and Krasnoselsky's random fixed point theo-rems.Using obtained results we also establish another theorem on existenceof random solution of random equations with P_1-compact operators.