Sahu, D. R. Applications of the \(S\)-iteration process to constrained minimization problems and split feasibility problems. (English) Zbl 1281.47053 Fixed Point Theory 12, No. 1, 187-204 (2011). 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. Cited in 4 ReviewsCited in 60 Documents 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 Keywords:accretive operator; nonexpansive mapping; sunny nonexpansive retraction; fixed point iterative algorithm; normal \(S\)-iteration process; rate of convergence of iterative algorithm; constrained optimization problem; split feasibility problem Citations:Zbl 1134.47047 PDFBibTeX XMLCite \textit{D. R. Sahu}, Fixed Point Theory 12, No. 1, 187--204 (2011; Zbl 1281.47053) Full Text: Link