The use of K-normed spaces gives us the possibility of proving that a fixed point theorem due to B. D. Lou [Proc. Amer. Math. Soc. 127 (1999), no. 8, 2259–2264; MR1646199 (99m:47065)] is equivalent to the Banach contraction principle. This confirms the conspiracy among fixed point theorems. Moreover, the theorem of Luo is improved and extended to different contexts. A counterexample about the fixed points of the sum of a contraction and an integral operator is given. The usefulness of the K-norm is tested on a Volterra integral equation as well

Fixed points for some non-obviously contractive operators

DE PASCALE, LUIGI
2002

Abstract

The use of K-normed spaces gives us the possibility of proving that a fixed point theorem due to B. D. Lou [Proc. Amer. Math. Soc. 127 (1999), no. 8, 2259–2264; MR1646199 (99m:47065)] is equivalent to the Banach contraction principle. This confirms the conspiracy among fixed point theorems. Moreover, the theorem of Luo is improved and extended to different contexts. A counterexample about the fixed points of the sum of a contraction and an integral operator is given. The usefulness of the K-norm is tested on a Volterra integral equation as well
DE PASCALE, E.; DE PASCALE, Luigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/72259
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