Variational Inclusions Involving Generalized Set-Valued Quasi-Contractive Mappings in Banach Spaces

  • Yangqing QiuEmail author
  • Hong Fang


In this paper, we give a characterization of strong convergence theorem of the Ishikawa iterative sequence with errors for the generalized set-valued variational inclusion problem involving a generalized set-valued quasi-contractive mapping in a real Banach space. First, the existence of the solution of the generalized set-valued variational inclusion problem is proved. Then, using the existence result, the Ishikawa iterative algorithm with errors is constructed and the convergence of the iterative sequences is proved. Finally, numerical experiments are proposed to support the main result. The results improve and extend some known results.


Variational inclusion Generalized quasi-contractive mapping Fixed point Iterative algorithm Convergence 

Mathematics Subject Classification

47H10 49J30 



This work was supported by the key discipline (Applied Mathematics) of Shanghai Polytechnic University (No. XXKPY1604).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no competing interests.

Author contributions

All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ScienceShanghai Polytechnic UniversityShanghaiChina

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