An iterative scheme for general mixed multivalued mildly nonlinear variational inequalities
type: Item
instance of: scholarly article
title: An iterative scheme for general mixed multivalued mildly nonlinear variational inequalities
zbMATH Open document ID: 0921.65047
author: Rais Ahmad
author: A. H. Siddiqi
author: M. Firdosh Khan
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1999-09-29T00:00:00Z
review text: Let \(H\) be a real Hilbert space whose inner product is denoted by \(\langle\cdot,\cdot\rangle\) and let \(K\) be a closed convex subset of \(H\). Let \(g:H\to H\) be a mapping and let \(T,A:H\to C(H)\) be multivalued mappings, where \(C(H)\) is the family of all nonempty compact subset of \(H\). The problem of finding \(u\in H\), \(x\in T(u)\) and \(y\in A(u)\) such that \(g(u)\in K\) and \[ \bigl\langle x-y,g(v)-g(u)\bigr \rangle+b \bigl(u,g(v)\bigr) -b\bigl(u, g(u) \bigr)\geq 0,\;\forall g(v)\in K, \] called the general mixed multivalued mildly nonlinear variational inequality problem, is considered. An iterative scheme is given to obtain an approximate solution of this problem. It is shown that the approximate solutions obtained by the iterative scheme converge strongly to the exact solution. Some special cases are dicussed, too.
reviewed by: Stefan Mititelu
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1281891
zbMATH Keywords: fixed point
zbMATH Keywords: convergence
zbMATH Keywords: Hilbert space
zbMATH Keywords: mixed multivalued mildly nonlinear variational inequality
zbMATH Keywords: iterative scheme
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1281891