Gauss-Seidel Type Iterative Algorithm for a Generalized System of Extended Non-linear Variational Inequalities

Authors

  • Fawzi F. M. Alhamdi Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia https://orcid.org/0000-0002-8734-5516
  • Nifeen H. Altaweel Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
  • Faizan Ahmad Khan Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
  • Saleem K. Aljuhani Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia

DOI:

https://doi.org/10.37256/cm.5320244595

Keywords:

generalized system of extended non-linear variational inequalities (GSENVI), relaxed (α, β)-cocoercitivity, lipschitz continuity, fixed point, projection technique, k-steps gauss-seidel type iterative algorithm

Abstract

This study is focused on a new generalized system of extended non-linear variational inequalities (GSENVI, for short) involving 3k-distinct non-linear relaxed cocoercive operators. We give the equivalent formulation of GSENVI in a more convenient form by using auxiliary principal technique. Through the projection technique, we demonstrate that the non-linear projection equations are analogous to equivalent form of GSENVI. By the use of alternative fixed point formulations, we proposed the k-steps Gauss-Seidel type iterative algorithms to obtain an approximate solution of the GSENVI. Further, we discuss the convergence of proposed k-step Gauss Seidel type iterative algorithms. Several special cases of GSENVI are discussed for the reliability of our findings.

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Published

2024-08-09

How to Cite

1.
F. M. Alhamdi F, H. Altaweel N, Khan FA, K. Aljuhani S. Gauss-Seidel Type Iterative Algorithm for a Generalized System of Extended Non-linear Variational Inequalities. Contemp. Math. [Internet]. 2024 Aug. 9 [cited 2024 Dec. 11];5(3):3038-60. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4595