A Halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces

Abstract

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.