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Zbl 0966.47040
Frigon, M.
Fixed point results for generalized contractions in gauge spaces and applications.
(English)
[J] Proc. Am. Math. Soc. 128, No.10, 2957-2965 (2000). ISSN 0002-9939; ISSN 1088-6826/e

The author presents fixed point results for generalized contractions defined on a complete gauge space $\bbfE$. He establishes that a generalized contraction $f:\bbfE\to \bbfE$ has a unique fixed point for a complete gauge space $\bbfE$. He also considers families of generalized contractions depending on a parameter $\{f^t: X\to\bbfE\}$ with $X\subset \bbfE$ closed. Finally, examples of applications of the previous fixed point results are also considered.
[S.K.Chatterjea (Kolkata)]
MSC 2000:
*47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N20 Appl. of operator theory to differential and integral equations
46A19 Generalizations of topological linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: generalized contractions; complete gauge space; unique fixed point

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