CAJ | 학술논문

首先在MengerPN-空间中引入锥理论，然后利用锥理论来讨论MengerPN-空间的增算子不动点问题，证明了①正规锥中，凝聚增算子存在不动点；②正则锥中，连续增算子存在不动点；③强极小锥中，增算子存在不动点。文章的结果不仅推广了Banach空间的相应结果，也丰富了MengerPN-空间中的理论。
수선재MengerPN-공간중인입추이론，연후이용추이론래토론MengerPN-공간적증산자불동점문제，증명료①정규추중，응취증산자존재불동점；②정칙추중，련속증산자존재불동점；③강겁소추중，증산자존재불동점。문장적결과불부추엄료Banach공간적상응결과，야봉부료MengerPN-공간중적이론。
In this article, the concept of cone in Menger PN-spaces isintroduced, then by using this concept, the existence of the fixed point for an increasing operator in Menger PN-spaces is discussed. And we verify that: ①there exist fixed points for the condensing and increasing operators in normed cone;②there exist fixed points for the continuous increasing operators in regular cone ;③there exist fixed points for the increasing operators in strong minimal cone. The results not only generalize the corresponding results in Banach spaces, but also enrich the theory of Menger PN-spaces.