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A Modified inertial Halpern method for solving split monotone variational inclusion problems in Banach Spaces

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Abstract

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solutions of split monotone variational inclusion problems which is also a fixed point problem of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Moreover, our iterative method uses stepsize which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We apply our result to solve split feasibility problems and display some numerical examples to show the performance of our result with the existing ones. The result present in this article unifies and extends several existing results in literature.

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Acknowledgements

The first author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Post-Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.

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Authors and Affiliations

  1. Department of Mathematics, University of Eswatini, Kwaluseni, South Africa

    G. C. Ugwunnadi

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    H. A. Abass PhD & O. K. Narain

  3. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, Pretoria, South Africa

    G. C. Ugwunnadi

  4. DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa

    H. A. Abass PhD

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  1. H. A. Abass PhD
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  2. G. C. Ugwunnadi
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  3. O. K. Narain
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The authors contributed equally in the development of this work. All the authors have read and approved the final manuscript.

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Correspondence to H. A. Abass PhD.

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Abass, H.A., Ugwunnadi, G.C. & Narain, O.K. A Modified inertial Halpern method for solving split monotone variational inclusion problems in Banach Spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 2287–2310 (2023). https://doi.org/10.1007/s12215-022-00795-y

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