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Strong convergence theorems for resolvents of accretive operators and nonexpansive mappings in Banach spaces. (English) Zbl 07347485

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
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