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On the split feasibility problem and fixed point problem of quasi-ϕ-nonexpansive mapping in Banach spaces

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Abstract

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.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11361070).

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Authors and Affiliations

  1. Department of General Education, The College of Arts and Sciences Yunnan Normal University, Kunming, 650222, Yunnan, People’s Republic of China

    Zhaoli Ma

  2. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, Yunnan, People’s Republic of China

    Lin Wang

  3. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Shih-sen Chang

Authors
  1. Zhaoli Ma
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  2. Lin Wang
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  3. Shih-sen Chang
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Correspondence to Lin Wang.

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Ma, Z., Wang, L. & Chang, Ss. On the split feasibility problem and fixed point problem of quasi-ϕ-nonexpansive mapping in Banach spaces. Numer Algor 80, 1203–1218 (2019). https://doi.org/10.1007/s11075-018-0523-1

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  • DOI: https://doi.org/10.1007/s11075-018-0523-1

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