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<p>In this paper, we propose and study a self-adaptive iterative method using golden ratio technique for solving variational inequality problem. We use Lyapunov functional to solve the underlying problem in a 2-uniformly convex Banach space. We obtain a weak convergence result when the cost operator is quasimonotone and locally Lipschitz continuous. Finally, we present numerical experiments to illustrate the applicability of our method. Our method extends some results in this direction in the literature.</p>

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A golden ratio self-adaptive algorithm for solving a quasimonotone variational inequality in banach spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月30日

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  • O. K. Oyewole,
  • O. J. Ogunsola,
  • S. P. Moshokoa

摘要

In this paper, we propose and study a self-adaptive iterative method using golden ratio technique for solving variational inequality problem. We use Lyapunov functional to solve the underlying problem in a 2-uniformly convex Banach space. We obtain a weak convergence result when the cost operator is quasimonotone and locally Lipschitz continuous. Finally, we present numerical experiments to illustrate the applicability of our method. Our method extends some results in this direction in the literature.