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.

Keywords

Split feasibility problem Quasi-ϕ-nonexpansive mapping Convergence Banach space 

Mathematics Subject Classification (2010)

47H09 47J25 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of General EducationThe College of Arts and Sciences Yunnan Normal UniversityKunmingPeople’s Republic of China
  2. 2.College of Statistics and MathematicsYunnan University of Finance and EconomicsKunmingPeople’s Republic of China
  3. 3.Center for General EducationChina Medical UniversityTaichungTaiwan

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