Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Keyword(s):
LetEbe a smooth Banach space with a norm·. LetV(x,y)=x2+y2-2 x,Jyfor anyx,y∈E, where·,·stands for the duality pair andJis the normalized duality mapping. We define aV-strongly nonexpansive mapping byV(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists aV-strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem.
Keyword(s):
1989 ◽
Vol 32
(1)
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pp. 90-97
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1999 ◽
Vol 4
(2)
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pp. 83-100
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Keyword(s):
1976 ◽
Vol 59
(1)
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pp. 65-65
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