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Applications of the \(S\)-iteration process to constrained minimization problems and split feasibility problems. (English) Zbl 1281.47053
Summary: In this paper, the \(S\)-iteration process introduced by R. P. Agarwal et al. [J. Nonlinear Convex Anal. 8, No. 1, 61–79 (2007; Zbl 1134.47047)] is further analyzed for contraction and nonexpansive mappings. It is shown, theoretically as well as numerically, that the \(S\)-iteration process is faster than the Picard and Krasnoselskij-Mann iteration processes for contraction operators. We also propose a new iterative algorithm and prove a strong convergence theorem for computing fixed points of nonexpansive operators in a Banach space. Our results are applied for finding solutions of constrained minimization problems and split feasibility problems. Our iteration methods are of independent interest.

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
65J15 Numerical solutions to equations with nonlinear operators
90C30 Nonlinear programming
Zbl 1134.47047
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