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Modified Hybrid Projection Methods with SP Iterations for Quasi-Nonexpansive Multivalued Mappings in Hilbert Spaces

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Abstract

In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial forward–backward method with the inertial technique term has a more effective convergence than that of the standard forward–backward method and Halpern algorithm.

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Authors and Affiliations

  1. School of Science, University of Phayao, Phayao, 56000, Thailand

    Watcharaporn Chaolamjiak & Damrongsak Yambangwai

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    Hasanen A. Hammad

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  1. Watcharaporn Chaolamjiak
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  2. Damrongsak Yambangwai
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  3. Hasanen A. Hammad
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All authors have contributed equally and significantly in writing this article.

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Correspondence to Hasanen A. Hammad.

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Communicated by Fatemeh Panjeh Ali Beik.

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Chaolamjiak, W., Yambangwai, D. & Hammad, H.A. Modified Hybrid Projection Methods with SP Iterations for Quasi-Nonexpansive Multivalued Mappings in Hilbert Spaces. Bull. Iran. Math. Soc. 47, 1399–1422 (2021). https://doi.org/10.1007/s41980-020-00448-9

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  • DOI: https://doi.org/10.1007/s41980-020-00448-9

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