Fixed point theorems for ordered contractive mappings on noncommutative Banach spaces. (English) Zbl 1166.47054
Summary: Introducing a concept of a noncommutative Banach space, we obtain several fixed point theorems for continuous or discontinuous ordered contractive maps in an ordered noncommutative Banach space. A sufficient condition for the fixed point to be unique is given.
MSC:
| 47H10 | Fixed-point theorems |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
