Inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and fixed point problems in Hilbert spaces

Abstract

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.

Keywords:

• Equilibrium problem
• fixed point
• pseudomonotone bifunction
• strong convergence
• subgradient extragradient method

Mathematics Subject Classification (2010):

• 47H05
• 47H07
• 47H10
• 54H25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the NSF of China [grant number 12171062] and the Natural Science Foundation of Chongqing [grant number CSTB2022NSCQ-JQX0004]. This work was supported by National Natural Science Foundation of China [11771063].