Open AccessOn strong convergence theorems for a viscosity-type extragradient method
Author(s) -
Lu-Chuan Ceng,
Chee Sheng Fong
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103033c
Subject(s) - mathematics , variational inequality , hilbert space , monotone polygon , banach space , convergence (economics) , fixed point , type (biology) , weak convergence , viscosity , pure mathematics , strongly monotone , mathematical analysis , computer science , ecology , physics , geometry , computer security , quantum mechanics , economics , asset (computer security) , biology , economic growth
In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and the variational inclusion problem with two accretive operators. We obtain a strong convergence theorem in the setting of Banach spaces. In terms of this theorem, we establish the strong convergence result for solving the fixed point problem (FPP) of an asymptotically nonexpansive mapping and the variational inequality problem (VIP) for an inverse-strongly monotone mapping in the framework of Hilbert spaces. Finally, this result is applied to deal with the VIP and FPP in an illustrating example.