A Self-Adaptive Inertial Subgradient Extragradient Method for Approximating Common Solutions of Bilevel Equilibrium and Inclusion Problems in Hilbert Spaces

Authors

  • Abdussemii Oluwatosin-Enitan Owolabi Kampala International University, Kampala, P.O. Box 20000, Uganda
  • Olawale Kazeem Oyewole Tshwane University of Technology, Arcadia, Pretoria, PMB 007, South Africa
  • Hammed Anuoluwapo Abass efako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa
  • Seithuti Philemon Moshokoa Tshwane University of Technology, Arcadia, Pretoria, PMB 007, South Africa

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.6920

Keywords:

\keywords{Bilevel Equilibrium problem, pseudomonotone operator, Inertial technique, subgradient extragradient}

Abstract

In this paper, we study bilevel equilibrium (with a pseudomonotone bifunction) and inclusion problems in the framework of Hilbert spaces. We propose an inertial subgradient extragradient algorithm with self-adaptive step size for finding common solutions to the aforementioned problems. Unlike several existing works on inclusion problem in the literature, our under lying operator is monotone and Lipschitz continuous. Also, we also employ the use of inertial technique to accelerate the rate of strong convergence of the sequences generated by our proposed method. Moreover, the implementation of our proposed method does not require prior knowledge of the Lipschitz constant of the monotone operator. Furthermore, we give some numerical examples to illustrate the efficiency of our proposed algorithm.

Author Biographies

  • Abdussemii Oluwatosin-Enitan Owolabi, Kampala International University, Kampala, P.O. Box 20000, Uganda

    Department of Mathematics and Statistics, Lecturer (PhD)

  • Olawale Kazeem Oyewole, Tshwane University of Technology, Arcadia, Pretoria, PMB 007, South Africa

    Department of Mathematics and Statistics, Lecturer(PhD)

  • Hammed Anuoluwapo Abass, efako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa

    Department of Mathematics and Applied Mathematics, Post doctoral fellow

  • Seithuti Philemon Moshokoa, Tshwane University of Technology, Arcadia, Pretoria, PMB 007, South Africa

    Department of Mathematics and Statistics, Professor

References

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Published

2026-02-20

Issue

Vol. 19 No. 1: (January 2026)

Section

Mathematical Analysis

License

Copyright (c) 2026 Abdussemii Oluwatosin-Enitan Owolabi, Olawale Kazeem Oyewole, Hammed Anuoluwapo Abass, Seithuti Philemon Moshokoa

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How to Cite

A Self-Adaptive Inertial Subgradient Extragradient Method for Approximating Common Solutions of Bilevel Equilibrium and Inclusion Problems in Hilbert Spaces. (2026). European Journal of Pure and Applied Mathematics, 19(1), 6920. https://doi.org/10.29020/nybg.ejpam.v19i1.6920