A double inertial extragradient algorithm with self-adaptive stepsizes for solving variational inequalities and fixed point problems
Fixed Point Methods and Optimization, Volume 3, Issue 1, April 2026, Pages 60–75
XIAN-JUN LONG
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China
SI-JIE YU
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China
ZAI-YUN PENG
School of Mathematics, Yunnan Normal University, Kunming, 650092, P.R. China
Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Kunming, 650500, P.R. China
YEKINI SHEHU
School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, P.R. China
SIMEON REICH
Department of Mathematics, The Technion-Israel Institute of Technology, 3200003 Haifa, Israel
Abstract
In this paper, we present a double inertial extragradient algorithm with self-adaptive stepsizes for finding a common solution of a pseudomonotone variational inequality and a fixed point problem with a quasi-nonexpansive mapping in Hilbert spaces. The self-adaptive stepsize rule allows the stepsizes to increase and converge, which may accelerate the convergence of the algorithm. We establish strong convergence theorems under some modern conditions. Some numerical experiments illustrate the performances and advantages of our proposed algorithm.
Cite this Article as
Xian-Jun Long, Si-Jie Yu, Zai-Yun Peng, Yekini Shehu, and Simeon Reich, A double inertial extragradient algorithm with self-adaptive stepsizes for solving variational inequalities and fixed point problems, Fixed Point Methods and Optimization, 3(1), 60–75, 2026