On the split feasibility problem and fixed point problem of quasi-ϕ-nonexpansive mapping in Banach spaces
The purpose of this paper is to propose an algorithm to solve the split feasibility and fixed point problem of quasi-ϕ-nonexpansive mappings in Banach spaces. Without the assumption of semi-compactness on the mappings, it is proved that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the split feasibility and fixed point problems. As applications, the main results presented in this paper are used to study the convexly constrained linear inverse problem and split null point problem. Finally, a numerical example is given to support our results. The results presented in the paper are new and improve and extend some recent corresponding results.
KeywordsSplit feasibility problem Quasi-ϕ-nonexpansive mapping Convergence Banach space
Mathematics Subject Classification (2010)47H09 47J25
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This work was supported by the National Natural Science Foundation of China (Grant No. 11361070).
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