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New Algorithms for a Class of Accretive Variational Inequalities in Banach Spaces

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Abstract

In this paper, for finding a common zero of a finite family of m-accretive mappings in uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm, we propose an implicit iteration algorithm and an explicit one, based on a convex combination of the steepest-descent method and a composition of resolvents. We also show that our main algorithm contains some iterative ones in literature as special cases. Finally, we give numerical examples for illustration.

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Funding

This work was supported by the Vietnam National Foundation for Science and Technology Development under grant no. 101.02-2017.305.

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Authors and Affiliations

  1. Duy Tan University, 13 Quang Trung, Da Nang, Vietnam

    Nguyen Buong

  2. Institute of Information Technology, Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, Ha Noi, Vietnam

    Nguyen Buong

  3. Binh Phuoc Teacher’s Training College, Binh Phuoc, Vietnam

    Than Van Dinh

  4. Thai Nguyen National University, Thai Nguyen, Vietnam

    Tran Thi Huong

Authors
  1. Nguyen Buong
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  2. Than Van Dinh
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  3. Tran Thi Huong
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Correspondence to Nguyen Buong.

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Buong, N., Van Dinh, T. & Huong, T.T. New Algorithms for a Class of Accretive Variational Inequalities in Banach Spaces. Acta Math Vietnam 45, 767–781 (2020). https://doi.org/10.1007/s40306-019-00355-0

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  • DOI: https://doi.org/10.1007/s40306-019-00355-0

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