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Iterative methods for convex proximal split feasibility problems and fixed point problems

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Abstract

In this paper we prove strong convergence result for a problem of finding a point which minimizes a proper convex lower-semicontinuous function f which is also a fixed point of a total asymptotically strict pseudocontractive mapping such that its image under a bounded linear operator A minimizes another proper convex lower-semicontinuous function g in real Hilbert spaces. In our result in this work, our iterative scheme is proposed with a way of selecting the step-size such that its implementation does not need any prior information about the operator norm ||A|| because the calculation or at least an estimate of the operator norm ||A|| is very difficult, if it is not an impossible task. Our result complements many recent and important results in this direction.

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Authors and Affiliations

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

    Yekini Shehu

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  1. Yekini Shehu
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Shehu, Y. Iterative methods for convex proximal split feasibility problems and fixed point problems. Afr. Mat. 27, 501–517 (2016). https://doi.org/10.1007/s13370-015-0344-5

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  • DOI: https://doi.org/10.1007/s13370-015-0344-5

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