Weak convergence theorems for strictly pseudocontractive mappings and generalized mixed equilibrium problems. (English) Zbl 1381.47050

Jung, Jong Soo

J. Appl. Math. 2012, Article ID 384108, 18 p. (2012).

Summary: We introduce a new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-strongly-monotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme converges weakly to a common element of the above three sets under suitable control conditions. The results in this paper substantially improve, develop, and complement the previous well-known results in this area.

MSC:

47J25	Iterative procedures involving nonlinear operators
47H05	Monotone operators and generalizations
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

iterative method; strictly pseudocontractive mapping; inverse-strongly-monotone mapping; Hilbert spaces

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