Jung, Jong Soo Strong convergence theorems for resolvents of accretive operators and nonexpansive mappings in Banach spaces. (English) Zbl 07347485 J. Nonlinear Convex Anal. 21, No. 1, 31-47 (2020). Summary: We introduce a new iterative algorithm for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping in a real uniformly convex Banach space having a uniformly Gâteaux differentiable norm. Strong convergence of the sequence generated by proposed algorithm to a common point of two sets is established under mild control conditions. MSC: 47H06 Nonlinear accretive operators, dissipative operators, etc. 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H10 Fixed-point theorems 47J25 Iterative procedures involving nonlinear operators 49M05 Numerical methods based on necessary conditions 65J15 Numerical solutions to equations with nonlinear operators Keywords:iterative algorithm; accretive operator; resolvent; zeros; nonexpansive mappings; fixed points; variational inequalities; uniformly Gâteaux differentiable norm; uniformly convex PDFBibTeX XMLCite \textit{J. S. Jung}, J. Nonlinear Convex Anal. 21, No. 1, 31--47 (2020; Zbl 07347485) Full Text: Link