A modified iterative algorithm for split feasibility problems of right Bregman strongly quasi-nonexpansive mappings in Banach spaces with applications. (English) Zbl 1466.47046
Summary: In this paper, we present a new iterative scheme for finding a common element of the solution set \(\mathcal F\) of the split feasibility problem and the fixed point set \(F(T)\) of a right Bregman strongly quasi-nonexpansive mapping \(T\) in \(p\)-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real \(p\)-uniformly convex and uniformly smooth Banach spaces. Furthermore, we give some examples and applications to illustrate our main results in this paper. Our results extend and improve the recent ones of some others in the literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 90C25 | Convex programming |
| 90C48 | Programming in abstract spaces |
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