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In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.
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참고문헌 (16)
참고문헌 신청
E. Blum / 1994 / From optimization and variational inequalities to equilibrium problems / Math. Student 63(1-4):123~145
F. E. Browder / 1965 / Fixed point theorems for noncompact mappings in Hilbert space / Proc. Natl. Acad. Sci. (USA) 53:1272~1276
L. C. Ceng / 2011 / Some iterative methods for finding fixed points and solving constrained convex minimization problems / Nonlinear Anal 74(16):5286~5802
L. C. Ceng / 2007 / Iterative construction of fixed points of nonselfmappings in Banach spaces / J. Comput. Appl. Math 206(2):814~825
F. Cianciaruso / 2010 / Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert space / J. Optim. Theory Appl 146(2):491~509
F. E. Browder / 1965 / Fixed point theorems for noncompact mappings in Hilbert space / Proc. Natl. Acad. Sci. (USA) 53:1272~1276
L. C. Ceng / 2011 / Some iterative methods for finding fixed points and solving constrained convex minimization problems / Nonlinear Anal 74(16):5286~5802
L. C. Ceng / 2007 / Iterative construction of fixed points of nonselfmappings in Banach spaces / J. Comput. Appl. Math 206(2):814~825
F. Cianciaruso / 2010 / Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert space / J. Optim. Theory Appl 146(2):491~509
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