An algorithm with general errors for the zero point of monotone mappings in Banach spaces

Tang, Yan; Bao, Zhi-Qing; Wen, Dao-Jun

doi:10.1186/1029-242x-2014-484

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2016

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“…The problem (1.2) is very interesting as it is connected with the fixed point problem for nonlinear mapping and the problem of finding a zero point of an accretive operator in Banach spaces (see [4]). For the problem of finding a zero point of a nonlinear mapping (see [5,6,7]). In 2010, Yao et al [8] introduced the following system of general variational inequalities in Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

Strong convergence of a viscosity iterative algorithm in Banach spaces with applications

Imnang¹,

Suantai²

2016

ams

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We present the strong convergence theorems for the viscosity iterative scheme for finding a common element of the solution set of the system of general variational inequalities for two arbitrary nonlinear mappings and the fixed point set of a nonexpansive mapping in real 2uniformly smooth and uniformly convex Banach spaces. Furthermore, we apply our main result with the problem of approximating a zero point of accretive operators and a fixed point of strictly pseudocontractive mappings in Banach spaces. The main results presented in this paper improve and extend some results in the literature.

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