, Volume 149, Issue 2, pp 239-253

Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings

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Abstract

We deal with a common fixed point problem for a family of quasinonexpansive mappings defined on a Hilbert space with a certain closedness assumption and obtain strongly convergent iterative sequences to a solution to this problem. We propose a new type of iterative scheme for this problem. A feature of this scheme is that we do not use any projections, which in general creates some difficulties in practical calculation of the iterative sequence. We also prove a strong convergence theorem by the shrinking projection method for a family of such mappings. These results can be applied to common zero point problems for families of monotone operators.

The first author and the second author are supported by Grant-in-Aid for Scientific Research No. 22540175 and No. 19540167 from Japan Society for the Promotion of Science, respectively. The third author is supported by the Grant NSC 99-2115-M-110-004-MY3.