A Halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces. (English) Zbl 1497.47092
Summary: We study the split feasibility problem (SFP) involving the fixed point problems (FPP) in the framework of \(p\)-uniformly convex and uniformly smooth Banach spaces. We propose a Halpern-type iterative scheme for solving the solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then we prove its strong convergence theorem of the sequences generated by our iterative scheme under implemented conditions. We finally provide some numerical examples and demonstrate the efficiency of the proposed algorithm. The obtained result of this paper complements many recent results in this direction.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
split feasibility problem; Bregman relatively nonexpansive semigroup; Halpern-type iterative scheme; strong convergence; fixed point problemReferences:
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