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A general alternative regularization method with line search technique for solving split equilibrium and fixed point problems in Hilbert spaces

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Abstract

In this paper, we introduce a new general alternative regularization algorithm for solving split equilibrium and fixed point problems in real Hilbert spaces. The proposed method does not require a prior estimate of the norm of the bounded linear operator nor a fixed stepsize for its convergence. Instead, we employ a line search technique and prove a strong convergence result for the sequence generated by the algorithm. A numerical experiment is given to show that the proposed method converges faster in terms of number of iteration and CPU time of computation than some existing methods in the literature.

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Acknowledgements

L. O. Jolaoso is supported by the Postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa. He acknowledge with thanks the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria, 0204, South Africa

    Lateef Olakunle Jolaoso

  2. Department of Mathematics, Faculty of Science, Erzurum Technical University, 25700, Erzurum, Turkey

    Ibrahim Karahan

Authors
  1. Lateef Olakunle Jolaoso
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  2. Ibrahim Karahan
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Correspondence to Lateef Olakunle Jolaoso.

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Communicated by Carlos Conca.

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Jolaoso, L.O., Karahan, I. A general alternative regularization method with line search technique for solving split equilibrium and fixed point problems in Hilbert spaces. Comp. Appl. Math. 39, 150 (2020). https://doi.org/10.1007/s40314-020-01178-8

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  • DOI: https://doi.org/10.1007/s40314-020-01178-8

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