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A new iterative algorithm for common solutions of a finite family of accretive operators. (English) Zbl 1218.47101
Summary: The purpose in this paper is to prove strong convergence to a common solution for a finite family of accretive operators in a strictly convex Banach space by means of a new iterative algorithm, thus generalizing and extending the results of [T.-H. Kim and H.-K. Xu, Nonlinear Anal., Theory Methods Appl. 61, No. 1–2, A, 51–60 (2005; Zbl 1091.47055)] and [H. Zegeye and N. Shahzad, ibid. 66, No. 5, A, 1161–1169 (2007; Zbl 1120.47061)]. Furthermore, strong convergence to a common fixed point is discussed for a finite family of pseudocontractive mappings under certain conditions.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
47H09Mappings defined by “shrinking” properties