Form equivalence class Howard-Rubin Number: 0
Statement:
Caristi's Fixed Point Theorem: If \((X,\rho)\) is a complete metric space and \(\phi : X\rightarrow{\Bbb R}\) is bounded above and upper semi-continuous then in the Br\ondsted ordering(\(x\le y\) iff \(\rho(x,y)\le\phi(y) - \phi(x))\) every \(f: X\rightarrow X\)satisfying \(\forall t\in X\), \(t\le f(t)\) has a fixed point.
Howard-Rubin number: 0 L
Citations (articles):
Caristi [1976]
Fixed point theorems for mappings satisfying inwardness conditions
Manka [1998a]
Some forms of the axiom of choice
Connections (notes):
Note [38]
Definitions from Manka [1988a] and Manka [1988b]
References (books):
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