Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

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Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly Fan Shop - NHL - Hats pseudocontractive mapping in a real Hilbert space.Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process.Via suitable assumptions, it is shown that the sequences generated by such a method converge Can Punch / Bottle Openers strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).