Geodesic
Approximation of solutions to a general system of variational inclusions in Banach spaces and applications
Liu, Hongbo 1 ; Long, Qiang 1 ; Li, Yi 2
1 School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
2 School of Science, Southwest University of Science and Technology, China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 644-657.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a $\lambda$-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented.
DOI : 10.22436/jnsa.011.05.06
Classification : 47J05, 47H09, 49J25
Keywords: General system of variational inclusions, forward-backward splitting method, invex set, resolvent operator, strictly pseudocontractive

Liu, Hongbo  1 ; Long, Qiang  1 ; Li, Yi  2

1 School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
2 School of Science, Southwest University of Science and Technology, China 
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Liu, Hongbo ; Long, Qiang ; Li, Yi . Approximation of solutions to a general system of  variational inclusions in Banach spaces and applications. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 644-657. doi : 10.22436/jnsa.011.05.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.05.06/

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