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Convergence analysis for proximal split feasibility problems and fixed point problems

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Abstract

Our aim in this paper is to introduce iterative algorithms and prove their strong convergence for solving proximal split feasibility problems and fixed point problems for \(k\)-strictly pseudocontractive mappings in Hilbert spaces. The sequence generated by our first iterative scheme converges strongly to an approximate common solution of convex minimization feasibility problem and fixed point problem. Furthermore, our second algorithm generates a strongly convergent sequence to an approximate common solution of non-convex minimization feasibility problem and fixed point problem. In all our results in this work, our iterative schemes are proposed with a way of selecting the step-sizes such that their implementation does not need any prior information about the operator norm because the calculation or at least an estimate of the operator norm \(||A||\) is very difficult, if not an impossible task. Our result complements many recent and important results in this direction.

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Acknowledgments

The authors are very grateful to the Editor in charge of the manuscript and the two anonymous referees for many insightful, detailed and helpful comments which led to significant improvement of the previous version of paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu & Ferdinard U. Ogbuisi

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  1. Yekini Shehu
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  2. Ferdinard U. Ogbuisi
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Correspondence to Yekini Shehu.

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Shehu, Y., Ogbuisi, F.U. Convergence analysis for proximal split feasibility problems and fixed point problems. J. Appl. Math. Comput. 48, 221–239 (2015). https://doi.org/10.1007/s12190-014-0800-7

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  • DOI: https://doi.org/10.1007/s12190-014-0800-7

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