(untitled) (European Journal of Pure and Applied Mathematics, 2026)
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.