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Convergence of a hybrid viscosity approximation method for finding zeros of m-accretive operators

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Abstract

For finding a zero of an m-accretive operator in a real Banach space, we consider an implicit hybrid viscosity approximation method and show that its explicit variant converges strongly to a zero under weaker assumptions than the ones used recently by Ceng et al. (Numer. Func. Anal. Opt. 35(2), 142–165, 2012). First, we examine the case of spaces which are uniformly smooth or reflexive and strictly convex with a uniformly Gâteaux differentiable norm. Afterwards, we improve our convergence results when the space is uniformly convex. Furthermore, we show that the strong convergence of some modified Halpern and Krasnosel’skii–Mann type methods can also be deduced from our results. Finally, a numerical example is also given to illustrate the convergence analysis of the considered method.

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Acknowledgements

This work was supported by Natural Science Fund of Vietnam Ministry of Education and Training (No. B2018-TNA-62). The research of the third author is supported by the Namur Institute for Complex Systems (naXys, University of Namur, Belgium).

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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nguyen Thi Thu Thuy

  2. Faculty of Basic Science, Thai Nguyen University of Agriculture and Foresty, Thai Nguyen University, Thai Nguyen, Vietnam

    Pham Thanh Hieu

  3. Namur Institute for Complex Systems, Department of Mathematics, University of Namur, Namur, Belgium

    J. J. Strodiot

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  1. Nguyen Thi Thu Thuy
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  2. Pham Thanh Hieu
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  3. J. J. Strodiot
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Correspondence to J. J. Strodiot.

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Thuy, N.T.T., Hieu, P.T. & Strodiot, J.J. Convergence of a hybrid viscosity approximation method for finding zeros of m-accretive operators. Numer Algor 83, 1591–1612 (2020). https://doi.org/10.1007/s11075-019-00740-8

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