Strong convergence theorems for solving a general system of finite variational inequalities for finite accretive operators and fixed points of nonexpansive semigroups with weak contraction mappings
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Author list: Onjai-Uea N., Katchang P., Kumam P.
Publisher: SpringerOpen
Publication year: 2012
Journal: Fixed Point Theory and Applications (1687-1820)
Volume number: 2012
ISSN: 1687-1820
eISSN: 1687-1812
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we prove a strong convergence theorem for finding a common solution of a general system of finite variational inequalities for finite different inverse-strongly accretive operators and solutions of fixed point problems for a nonexpansive semigroup in a Banach space based on a viscosity approximation method by using weak contraction mappings. Moreover, we can apply the above results to find the solutions of the class of k-strictly pseudocontractive mappings and apply a general system of finite variational inequalities into a Hilbert space. The results presented in this paper extend and improve the corresponding results of Ceng et al. (2008), Katchang and Kumam (2011), Wangkeeree and Preechasilp (2012), Yao et al. (2010) and many other authors. ฉ 2012 Onjai-uea et al.; licensee Springer.
Keywords
General system of finite variational inequalities, Inverse-strongly accretive operator, Nonexpansive semigroups, Sunny nonexpansive retraction, Weak contraction
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