Abstract
In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Banach spaces and also operators having properties weaker than lower semicontinuity. Our results either extend or improve corresponding ones present in literature.
Highlights
Fixed point theorems are a very powerful tool of the current mathematical applications
The main aim of this work is to establish random fixed point theorems under mild continuity assumptions
By using the approximation method which is due to Ionescu Tulcea, we provide a new proof for the random version of Ky Fan’s fixed point theorem
Summary
Fixed point theorems are a very powerful tool of the current mathematical applications. It states the existence of the random fixed points for the almost lower semicontinuous operators defined on Banach spaces. 4 Random fixed point theorems for lower semicontinuous operators This section is designed to extending the results established in [ ] by considering lower semicontinuous operators defined on Fréchet spaces.
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