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The Split Feasibility Problem with Some Projection Methods in Banach Spaces

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  • Toshiharu Kawasaki
  • Hiroko Manaka

Abstract

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

Suggested Citation

  • Toshiharu Kawasaki & Hiroko Manaka, 2020. "The Split Feasibility Problem with Some Projection Methods in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:2913087
    DOI: 10.1155/2020/2913087
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    References listed on IDEAS

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    1. Y. Alber & D. Butnariu, 1997. "Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 33-61, January.
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