Abstract
AbstractIn this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr’s common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces.
Highlights
In recent years, there was an surge of interest in the study of electrorheological fluids, sometimes referred to as ‘smart fluids’
The purpose of this paper is to discuss the existence of common fixed points of mappings defined on subsets of modular vector spaces, as introduced by Nakano [ ] which are natural generalizations of many classical function spaces
We introduce the concept of Banach operator pairs [, ] in modular vector spaces
Summary
There was an surge of interest in the study of electrorheological fluids, sometimes referred to as ‘smart fluids’ (for instance lithium polymetachrylate). The purpose of this paper is to discuss the existence of common fixed points of mappings defined on subsets of modular vector spaces, as introduced by Nakano [ ] which are natural generalizations of many classical function spaces.
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