Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces

Volume 9, Issue 6, pp 4039--4051 http://dx.doi.org/10.22436/jnsa.009.06.48

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Authors

Qian Yan - School of Mathematics Science, Chongqing Normal University, Chongqing 401331, China. Gang Cai - School of Mathematics Science, Chongqing Normal University, Chongqing 401331, China. Ping Luo - School of Mathematics Science, Chongqing Normal University, Chongqing 401331, China.

Abstract

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality problems in Hilbert spaces. Finally, we also give one numerical example to support our main results.

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Keywords

• Fixed point
• generalized implicit rules
• generalized contraction
• nonexpansive mapping
• Banach spaces.

MSC

•  49H09
•  47H10
•  47H17
•  49M05

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