Convergence Theorems for Generalized Viscosity Explicit Methods for Nonexpansive Mappings in Banach Spaces and Some Applications
Keyword(s):
In this paper, we introduce a generalized viscosity explicit method (GVEM) for nonexpansive mappings in the setting of Banach spaces and, under some new techniques and mild assumptions on the control conditions, prove some strong convergence theorems for the proposed method, which converge to a fixed point of the given mapping and a solution of the variational inequality. As applications, we apply our main results to show the existence of fixed points of strict pseudo-contractions and periodic solutions of nonlinear evolution equations and Fredholm integral equations. Finally, we give some numerical examples to illustrate the efficiency and implementation of our method.
2014 ◽
Vol 14
(4-5)
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pp. 969-1000
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Keyword(s):
1970 ◽
Vol 148
(1)
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pp. 273
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1991 ◽
Vol 17
(11)
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pp. 1085-1092
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Keyword(s):
1971 ◽
Vol 155
(2)
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pp. 409-409
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Keyword(s):
1970 ◽
Vol 32
(1)
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pp. 269-281
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1970 ◽
Vol 148
(1)
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pp. 273-273
2010 ◽
Vol 11
(1)
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pp. 1-41
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