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Single-step algorithm for variational inequality problems in 2-uniformly convex banach spaces

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Abstract

In this work, we prove weak convergence of a single-step iterative algorithm to a solution of variational inequality problems in 2-uniformly convex and uniformly smooth real Banach spaces. We apply our main result to the Nash-Cournot equilibrium oligopoly electricity market. We also give some numerical examples in infinite dimensional setting to illustrate how our algorithm works. Finally, our results generalize and complement several existing results in the literature.

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Acknowledgements

The authors appreciate the support of their institution and AfDB.

Funding

This work is supported from AfDB Research Grant Funds to AUST.

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Authors and Affiliations

  1. Mathematics Institute African University of Science and Technology, Abuja, Nigeria

    A. U. Bello, H. Yusuf & N. Djitte

  2. Department of Mathematics, Federal University Dutsinma, Dutsinma, Kastina State, Nigeria

    A. U. Bello

  3. Gaston Berger University, Saint Louis, Senegal

    N. Djitte

Authors
  1. A. U. Bello
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  2. H. Yusuf
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  3. N. Djitte
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All authors contributed equally.

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Correspondence to A. U. Bello.

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Bello, A.U., Yusuf, H. & Djitte, N. Single-step algorithm for variational inequality problems in 2-uniformly convex banach spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1463–1481 (2023). https://doi.org/10.1007/s12215-022-00746-7

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