Variational-like inequalities for multivalued maps
type: Item
instance of: scholarly article
title: Variational-like inequalities for multivalued maps
zbMATH Open document ID: 0929.49003
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2000-01-18T00:00:00Z
review text: The authors investigate the variational-like inequality Problem (P) To find \(x_0\in K\) such that for each \(y\in K\) there exists \(u_0\in T(x_0)\;\) fulfilling \[ \langle M(x_0,u_0),\eta(y,x_0)\rangle + b(x_0,y)-b(x_0,x_0)\geq 0, \] where \(K\) is a nonempty subset of a reflexive Banach space \(X,\) \(T:K\to 2^C\) a multivalued map, \(C\) a nonempty subset of a dual \(X^*,\;M:K\times C\to X^*,\;\eta:K\times K\to X,\;b:K\times K\to \mathbb R,\;\langle.,.\rangle\) is the duality pairing between \(X^*\) and \(X.\) They generalize the monotonicity and hemicontinuity properties for multivalued maps. The main result is the existence theorem for Problem (P). The special case \(h(x,y)=b(y)\) is also considered.
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1275960
zbMATH Keywords: variational-like inequalities
zbMATH Keywords: multivalued map
zbMATH Keywords: Banach space
zbMATH Keywords: convex set
zbMATH Keywords: monotonicity
zbMATH Keywords: hemicontinuity
author: A. H. Siddiqi
author: Qamrul Hasan Ansari
author: M. Firdosh Khan
reviewed by: Igor Bock
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1275960