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Inertial Mann type algorithms for a finite collection of equilibrium problems and fixed point problem of demicontractive mappings

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Abstract

The aim of this paper is to study sequential and parallel inertial algorithms for approximating the common solution of a finite collection of equilibrium problems and a fixed point problem involving demicontractive mappings. We introduce the iterative methods based on the Mann type iteration and prove weak convergence results under the reasonable condition on the control parameters. We also give a numerical example to support our main results for the proposed algorithms.

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The Matlab codes used in the calculations are available from the corresponding author upon request.

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Acknowledgements

The authors are thankful to the two anonymous reviewers for their comments and suggestions to revise the paper into its present form.

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Author notes

  1. Prashanta Majee, Sonu Bai and Sahadeo Padhye contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, UP, 211004, India

    Prashanta Majee, Sonu Bai & Sahadeo Padhye

Authors
  1. Prashanta Majee
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  2. Sonu Bai
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  3. Sahadeo Padhye
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Correspondence to Prashanta Majee.

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Communicated by S. Ponnusamy.

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Majee, P., Bai, S. & Padhye, S. Inertial Mann type algorithms for a finite collection of equilibrium problems and fixed point problem of demicontractive mappings. J Anal 32, 447–469 (2024). https://doi.org/10.1007/s41478-023-00660-w

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  • DOI: https://doi.org/10.1007/s41478-023-00660-w

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