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In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.
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참고문헌 (20)
참고문헌 신청
Komi Afassinou / 2020 / ITERATIVE ALGORITHM FOR APPROXIMATING SOLUTIONS OF SPLIT MONOTONE VARIATIONAL INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS IN REAL HILBERT SPACES / Nonlinear Functional Analysis and Applications 25(3):491~510
R. P. Agarwal / 2009 / Fixed point theory for Lipschitzian-type mappings with applications / Springer
F.E Browder / 1967 / Construction of fixed points of nonlinear mappings in Hilbert space / Journal of Mathematical Analysis and Applications 20(2):197~228
Tanom Chamnarnpan / 2012 / A new iterative method for a common solution of fixed points for pseudo-contractive mappings and variational inequalities / Fixed Point Theory and Applications 2012(1):15
Hideaki Iiduka / 2005 / Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings / Nonlinear Analysis: Theory, Methods & Applications 61(3):341~350
R. P. Agarwal / 2009 / Fixed point theory for Lipschitzian-type mappings with applications / Springer
F.E Browder / 1967 / Construction of fixed points of nonlinear mappings in Hilbert space / Journal of Mathematical Analysis and Applications 20(2):197~228
Tanom Chamnarnpan / 2012 / A new iterative method for a common solution of fixed points for pseudo-contractive mappings and variational inequalities / Fixed Point Theory and Applications 2012(1):15
Hideaki Iiduka / 2005 / Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings / Nonlinear Analysis: Theory, Methods & Applications 61(3):341~350
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