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A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces

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Abstract

In this paper, we introduce a modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and split-equality fixed-point problem for Bregman quasi-nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We introduce a generalized step size such that the algorithm does not require a prior knowledge of the operator norms and prove a strong convergence theorem for the sequence generated by our algorithm. We give some applications and numerical examples to show the consistency and accuracy of our algorithm. Our results complement and extend many other recent results in this direction in literature.

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Acknowledgements

The authors thank the anonymous referee for valuable and useful suggestions and comments which led to the great improvement of the paper.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    A. Taiwo, L. O. Jolaoso & O. T. Mewomo

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  1. A. Taiwo
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  2. L. O. Jolaoso
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  3. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Communicated by Gabriel Haeser.

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Taiwo, A., Jolaoso, L.O. & Mewomo, O.T. A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces. Comp. Appl. Math. 38, 77 (2019). https://doi.org/10.1007/s40314-019-0841-5

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  • DOI: https://doi.org/10.1007/s40314-019-0841-5

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