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Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems

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Abstract

In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space. We prove strong convergence theorems for these algorithms and the conditions of the convergence are very weak comparing other algorithms for the hierarchical fixed point problems. Further, we derive some consequences from the main results. Finally, we present two academic numerical examples for comparing these two algorithms with the algorithm in Dong et al. (J Fixed Point Theory A 19(4):3097–3118, 2017), which illustrate the advantage of the proposed algorithms. The methods and results presented in this paper generalize and unify previously known corresponding methods and results of this area.

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Acknowledgements

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. Qiao-Li Dong is supported by the scientific research project of Tianjin Municipal Education Commission (no. 2018KJ253).

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Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong & Xiao-Huan Li

  2. Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

    K. R. Kazmi

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    K. R. Kazmi

  4. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Rehan Ali

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  1. Qiao-Li Dong
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  2. K. R. Kazmi
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  3. Rehan Ali
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  4. Xiao-Huan Li
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Correspondence to Qiao-Li Dong.

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Dong, QL., Kazmi, K.R., Ali, R. et al. Inertial Krasnosel’skiǐ–Mann type hybrid algorithms for solving hierarchical fixed point problems. J. Fixed Point Theory Appl. 21, 57 (2019). https://doi.org/10.1007/s11784-019-0699-6

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  • DOI: https://doi.org/10.1007/s11784-019-0699-6

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