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On strong convergence of Halpern’s method for quasi-nonexpansive mappings in Hilbert spaces. (English) Zbl 1483.47096

Summary: In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping \(T\) and a strongly quasi-nonexpansive mappings \(S\), defined in a Hilbert space, such that \(I - S\) is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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