Improved gradient method for monotone and lipschitz continuous mappings in banach spaces. Issue 2 (March 2017)

• Record Type: Journal Article
• Authors: NAKAJO, Kazuhide
• Is Part Of: Acta mathematica scientia. Volume 37:Issue 2(2017)
• Page Start: 342
• Page End: 354
• Publication Date: 2017-03
• Subjects: Variational inequality problem -- gradient method -- monotone operators -- 2-uniformly convex Banach space -- hybrid method; 49J40 -- 47J25 -- 47H05; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(17)30006-1
• Languages: English
• ISSNs: 0252-9602

Abstract

Abstract: Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and { A n }nɛN be a family of monotone and Lipschitz continuos mappings of C into E *. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for { A n } and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.