Completely Continuous Operators on Banach Spaces

Radu Precup
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Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 2 in Methods in Nonlinear Integral Equations, 2002, pp 25-34 from Springer

Abstract: Abstract In this chapter we define the notion of a completely continuous operator from a Banach space to another Banach space and we present some simple properties of the completely continuous operators. Next we prove Brouwer’s fixed point theorem. Finally, we prove the famous Schauder fixed point theorem which, like Banach’s contraction principle, represents a fundamental result in nonlinear analysis.

Keywords: Banach Space; Fixed Point Theorem; Continuous Operator; Bounded Subset; Finite Rank (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9986-3_3

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DOI: 10.1007/978-94-015-9986-3_3

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