Fixed point theorems for three new nonlinear mappings in Banach spaces (Q2884679)
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scientific article; zbMATH DE number 6039391
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed point theorems for three new nonlinear mappings in Banach spaces |
scientific article; zbMATH DE number 6039391 |
Statements
30 May 2012
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Banach space
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nonexpansive mapping
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nonspreading mapping
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hybrid mapping
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fixed point
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Fixed point theorems for three new nonlinear mappings in Banach spaces (English)
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Let \(X\) be a Banach space, \(C \subset X\) be a nonempty closed convex subset of \(X\) and let \(T: C\to C\) be a mapping. The authors give geometric conditions on \(X\) and metric conditions on \(T\) such that the following are equivalent: (a) \(T\) has a fixed point; (b) \(\{T^n (x)\} \) is bounded for some \(x\in C\).
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