On a new iterative method for solving equilibrium problems and fixed point problems



	On a new iterative method for solving equilibrium problems and fixed point problems


	Fixed Point Theory, Volume 25, No. 1, 2024, 419-434, February 1st, 2024 DOI: 10.24193/fpt-ro.2024.1.26 Authors: Maryam Yazdi and Saeed Hashemi Sababe Abstract: A new iterative algorithm is proposed for finding a common solution of an equilibrium problem and a fixed point problem. Then, a strong convergence theorem is proved. As a consequence, they can be obtained some strong convergence theorems for an equilibrium problem and a split common fixed point problem. The obtained theorems can be applied to solve an equilibrium problem and a split common null point problem. The results presented in this paper extend and improve some corresponding ones in the literature. Finally, a numerical example is given to show the validity of the algorithm. Key Words and Phrases: Equilibrium problem, iterative method, fixed point. 2010 Mathematics Subject Classification: 47H10, 47J25, 47H09, 65J15. Published on-line: February 1st, 2024. Fulltext pdf Back to volume's table of contents