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Strong convergence of inertial shrinking projection method for split best proximity point problem and mixed equilibrium problem

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Abstract

In this paper, we introduce an inertial shrinking projection algorithm to approximate a solution of the best proximity point problem in such a way that the image of its solution under a bounded linear operator is the solution of the mixed equilibrium problem in the framework of real Hilbert spaces. Strong convergence theorem of the proposed algorithm has been established. We also derive some consequences from our main result. Further, we give a numerical experiment to determine the performance and superiority of the proposed algorithm. Finally, a comparison has also been carried out of our algorithm with an existing method.

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Acknowledgements

The authors would like to thank the editor as well as the anonymous reviewers for their useful suggestions and comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, 202002, India

    Shamshad Husain & Mubashshir U. Khairoowala

  2. University Polytechnic, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, 202002, India

    Mohd Furkan

Authors
  1. Shamshad Husain
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  2. Mohd Furkan
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  3. Mubashshir U. Khairoowala
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Correspondence to Mubashshir U. Khairoowala.

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Communicated by Tanmoy Som.

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Husain, S., Furkan, M. & Khairoowala, M.U. Strong convergence of inertial shrinking projection method for split best proximity point problem and mixed equilibrium problem. J Anal (2024). https://doi.org/10.1007/s41478-023-00713-0

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  • DOI: https://doi.org/10.1007/s41478-023-00713-0

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