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Shehu, Yekini

Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications. (English) Zbl 1247.47073

J. Glob. Optim. 52, No. 1, 57-77 (2012).
Summary: We introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of the variational inequality problem for a co-coercive mapping in a real Hilbert space. Then, strong convergence of the scheme to a common element of the three sets is proved. Furthermore, new convergence results are deduced, and finally, we apply our results to solving optimization problems, and present other applications.

Cited in 2 Reviews
Cited in 14 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics

Keywords:

nonexpansive mappings; generalized mixed equilibrium problem; variational inequality; Hilbert spaces; nonexpansive mapping; co-coercive mapping; real Hilbert space; strong convergence
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\textit{Y. Shehu}, J. Glob. Optim. 52, No. 1, 57--77 (2012; Zbl 1247.47073)
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References:

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