On a fixed point theorem of Greguš (Q1079169)
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scientific article; zbMATH DE number 3962557
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a fixed point theorem of Greguš |
scientific article; zbMATH DE number 3962557 |
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On a fixed point theorem of Greguš (English)
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1986
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Let T and I be weakly-commuting mappings of a closed convex subset C of a Banach space X into C satisfying the inequality \(\| Tx-Ty\| \leq a\| Ix-Iy\| +(1-a)\max \{\| Tx-Ix\|\), \(\| Ty-Iy\| \}\) for all x,y in C, where \(0<a<1\). It is proved that if I is linear and non-expansive in C and such that the range of I contains the range of T, then T and I have a unique common fixed point in C.
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weakly-commuting mappings of a closed convex subset
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unique common fixed point
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