Open AccessGeneral viscosity implicit midpoint rule for nonexpansive mapping
Author(s) -
Shuja Rizvi Haider
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/fil2101225r
Subject(s) - mathematics , midpoint method , variational inequality , hilbert space , sequence (biology) , midpoint , convergence (economics) , nonlinear system , viscosity , extension (predicate logic) , limit of a sequence , work (physics) , iterative method , mathematical analysis , mathematical optimization , geometry , limit (mathematics) , computer science , mechanical engineering , genetics , physics , quantum mechanics , economics , biology , programming language , economic growth , engineering
In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under the certain conditions imposed on the sequence of parameters, strong convergence theorem is proved by the sequence generated by the proposed iterative scheme, which, in addition, is the unique solution of the variational inequality problem. Furthermore, we provide some applications to variational inequalities, Fredholm integral equations, and nonlinear evolution equations and give a numerical example to justify the main result. The results presented in this work may be treated as an improvement, extension and refinement of some corresponding ones in the literature.