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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.

##### MSC:
 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
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