The purpose of this paper is to prove fixed point results for certain types of countably asymptotically \(\Phi \)-nonexpansive (or countably \(\Phi \)-condensing) operators on locally convex spaces and satisfying additional asymptotic contractive-type conditions. These results allow us to obtain generalizations of recent fixed point theorems of Ben Amar, Isac, Németh, O’Regan, and Touati to locally convex spaces. As an application, we obtain the existence of positive eigenvalues of countably asymptotically \(\Phi \)-nonexpansive (or countably \(\Phi \)-condensing) operators in locally convex spaces. Also, we present Krasnosel’skii fixed point theorems of two nonlinear operators acting on locally convex spaces. These results are based on a generalized notion of the semi-inner product in Lumer’s sense and the axiomatic measure of noncompactness.

本文的目的是证明局部凸空间上某些类型的可数渐近\（\ Phi \）-非扩张（或可数\（\ Phi \）-压缩）算子的不动点结果，并满足附加渐近收缩型条件。这些结果使我们能够将Ben Amar，Isac，Németh，O'Regan和Touati的最近不动点定理推广到局部凸空间。作为应用，我们获得存在正特征值的正渐近值（（\ Phi \）-渐近（或渐进\（\ Phi \））-压缩）算子在局部凸空间中。另外，我们给出了作用在局部凸空间上的两个非线性算子的Krasnosel'skii不动点定理。这些结果是基于Lumer的半内积的广义概念和非紧缩的公理度量。