A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

Title & Authors
A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS IN REAL BANACH SPACES
Bai, Chuan-Zhi; Fang, Jin-Xuan;

Abstract
In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $\small{x^{*},\;y^{*},\;z^{*}\;\in\;E}$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $\small{E\;{\rightarrow}\;E,\;{\theta}}$ is zero element in Banach space E, and A : $\small{E\;{\rightarrow}\;{2^E}}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.
Keywords
system of nonlinear implicit variational inclusion;resolvent operator;m-accretive mapping;approximation-solvability;iterative algorithms;
Language
English
Cited by
1.
A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES,;;

대한수학회논문집, 2010. vol.25. 1, pp.129-137
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