SHRINKING PROJECTION METHOD FOR A CLASS OF SPLIT FEASIBILITY PROBLEMS WITH MULTIPLE OUTPUT SETS
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DOI:
https://doi.org/10.34238/tnu-jst.15226Abstract
This paper investigates the split variational inequality problem with multiple output sets in Hilbert spaces. This model extends the split feasibility problem with multiple output sets and is closely related to several important classes of split problems. To solve this problem, we propose a novel inertial multistep shrinking projection method employing self-adaptive parameters. A notable advantage of the proposed method is that it does not require any prior knowledge of the norms of the transfer operators. Under standard assumptions, we prove the strong convergence of the sequence generated by the method. In addition, several related split models, including the split common minimum point problem, the split common fixed-point problem, and the split equilibrium problem with multiple output sets, are shown to be special cases of the considered framework. This demonstrates the flexibility, generality, and applicability of the proposed approach to a broad class of split problem models arising in theory and applications.Downloads
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