General auxiliary problem principle and solvability of a class of nonlinear mixed variational inequalities involving partially relaxed monotone mappings

Rassias, TM; Verma, RU

dc.contributor.author	Rassias, TM	en
dc.contributor.author	Verma, RU	en
dc.date.accessioned	2014-03-01T01:17:56Z
dc.date.available	2014-03-01T01:17:56Z
dc.date.issued	2002	en
dc.identifier.issn	1331-4343	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14711
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0036001679&partnerID=40&md5=a88c394f14eb4d4961ff6fc3d93e571e	en
dc.subject	Approximate solution	en
dc.subject	Approximation-solvability	en
dc.subject	Cocoercive mapping	en
dc.subject	General auxiliary variational inequality problem	en
dc.subject	Partially relaxed monotone mapping	en
dc.subject	Strongly monotone mapping	en
dc.subject.classification	Mathematics	en
dc.subject.other	COMPLEMENTARITY-PROBLEMS	en
dc.subject.other	PROJECTION	en
dc.subject.other	DECOMPOSITION	en
dc.subject.other	CONVERGENCE	en
dc.title	General auxiliary problem principle and solvability of a class of nonlinear mixed variational inequalities involving partially relaxed monotone mappings	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	The approximation-solvability of the following class of nonlinear variational inequality (NVI) problems based on anew general auxiliary problem principle is presented: Find an element x* is an element of K such that <T(x),x-->x> + f(x) - f(x*) greater than or equal to 0 for all x is an element of K, where T : K --> H is a partially relaxed monotone mapping from a nonempty closed convex subset K of a real Hilbert space H into H, and f : K --> R is a continuous convex function on K. The general auxiliary problem principle is described as follows: for given iterate x(k) is an element of K and for a constant p > 0, determine x(k+1) such that (for k greater than or equal to 0) <pT(x(k)) + pL(x(k+1)) + h'(x(k+1)) - pL(x(k)) - h'(x(k)), x - x(k+1>) + P[f(x) - f(x(k+1))] greater than or equal to 0 for all x is an element of K, where L : K --> H is any mapping on K, h : K - R is a function on K and h' is the derivative of h.	en
heal.publisher	ELEMENT	en
heal.journalName	Mathematical Inequalities and Applications	en
dc.identifier.isi	ISI:000173815200017	en
dc.identifier.volume	5	en
dc.identifier.issue	1	en
dc.identifier.spage	163	en
dc.identifier.epage	170	en