Abstract
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 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 strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).
Highlights
Throughout this paper we assume that C is a nonempty, convex and closed subset of a real Hilbert space ( H, k · k), whose inner product is denoted by h·, ·i
Inspired by the research work of [23], we introduce two inertial-like subgradient algorithms with line-search process for solving Equation (1) with a Lipschitzian and pseudomonotone operator and the common fixed point problem (CFPP) of an asymptotically nonexpansive operator and a strictly pseudocontractive operator in H
A : H → H is sequentially weakly continuous on C, L-Lipschitzian pseudomonotone on H, and A(C )
Summary
Throughout this paper we assume that C is a nonempty, convex and closed subset of a real Hilbert space ( H, k · k), whose inner product is denoted by h·, ·i. Inspired by the research work of [23], we introduce two inertial-like subgradient algorithms with line-search process for solving Equation (1) with a Lipschitzian and pseudomonotone operator and the common fixed point problem (CFPP) of an asymptotically nonexpansive operator and a strictly pseudocontractive operator in H.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
