Vol. 22(2021) No. 2



  Pseudomonotone variational inequalities and fixed points
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Fixed Point Theory, Volume 22, No. 2, 2021, 543-558, July 1st, 2021

DOI: 10.24193/fpt-ro.2021.2.36

Authors: L.C. Ceng, A. Petrușel, X. Qin and J.C. Yao

Abstract: 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.

Key Words and Phrases: Inertial subgradient extragradient method, pseudomonotone variational inequality, nonexpansive mapping, strictly pseudocontractive mapping.

2010 Mathematics Subject Classification: 47H05, 90C30, 47H10.

Published on-line: July 1st, 2021.

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