A Generalization of a Fixed Point Theorem of Goebel, Kirk and Shimi
1976 ◽
Vol 19
(1)
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pp. 7-12
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Keyword(s):
In [7], Goebel, Kirk and Shimi proved the following:Theorem. Let X be a uniformly convex Banach space, K a nonempty bounded closed and convex subset of X, and F:K→K a continuous mapping satisfying for each x, y∈K:(1)where ai≥0 and Then F has a fixed point in K.In this paper we shall prove that this theorem remains true in any Banach space X, provided that K is a nonempty, weakly compact convex subset of X and has normal structure (see Definition 1 below).
1994 ◽
Vol 124
(1)
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pp. 23-31
2020 ◽
Vol 2020
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pp. 1-4
1992 ◽
Vol 53
(1)
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pp. 25-38
2005 ◽
Vol 2005
(11)
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pp. 1685-1692
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2005 ◽
Vol 72
(3)
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pp. 371-379
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1982 ◽
Vol 25
(3)
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pp. 339-343
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Keyword(s):
2006 ◽
Vol 74
(1)
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pp. 143-151
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Keyword(s):
1980 ◽
Vol 32
(2)
◽
pp. 421-430
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Keyword(s):
1984 ◽
Vol 37
(3)
◽
pp. 358-365
Keyword(s):