Pseudomonotone variational inequalities and fixed points
Lu-Chuan Ceng, Adrian Petruşel, Xiaolong Qin, Jen Chih Yao · Fixed Point Theory · 2021
We introduce two new iterative algorithms with line-search process for solving a variational inequality problem with pseudomonotone and Lipschitz continuous mapping and a common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping. The proposed algorithms are based on inertial subgradient extragradient method with line-search process, hybrid steepest-descent method, and viscosity approximation method. Under mild conditions, we prove strong convergence of the proposed algorithms in a real Hilbert space.