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An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping

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Abstract

In this paper, we introduce and study an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping which is the unique solution of the variational inequality problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

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Acknowledgments

The authors are very thankful to the referees for their constructive, detailed and helpful comments and suggestions toward the improvement of the manuscript.

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Correspondence to K. R. Kazmi.

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Kazmi, K.R., Rizvi, S.H. An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping. Optim Lett 8, 1113–1124 (2014). https://doi.org/10.1007/s11590-013-0629-2

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  • DOI: https://doi.org/10.1007/s11590-013-0629-2

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