Fixed-Point Theory on a Frechet Topological Vector Space
2011 ◽
Vol 2011
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pp. 1-9
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Keyword(s):
We establish some versions of fixed-point theorem in a Frechet topological vector spaceE. The main result is that every mapA=BC(whereBis a continuous map andCis a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Krasnoselskii fixed-point theorem. Our first result extend the well-known Krasnoselskii's fixed-point theorem forU-contractions and weakly compact mappings, while the second one, by assuming that the family{T(⋅,y):y∈C(M)whereM⊂EandC:M→Ea compactoperator}is nonlinearφequicontractive, we give a fixed-point theorem for the operator of the formEx:=T(x,C(x)).
2005 ◽
Vol 2005
(5)
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pp. 789-801
Keyword(s):
Keyword(s):
2020 ◽
Vol 19
(1)
◽
pp. 171-192
2021 ◽
Vol 23
(10)
◽
pp. 247-266
2013 ◽
Vol 2013
(1)
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pp. 39
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Keyword(s):