Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

Ravi P. Agarwal; Donal O'Regan; Ram U. Verma

doi:10.1515/GMJ.2005.1

Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

Ravi P. Agarwal, Donal O'Regan, Ram U. Verma

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K₁ and K₂ be nonempty closed convex subsets of real Hilbert spaces H₁ and H₂, respectively. The two-step SNVI problem considered here is as follows: find an element (x^*; y^*) ∈ H₁ × H₂ such that (g(x^*); g(y^*)) ∈K₁ × K₂ and (formula omitted) are nonlinear mappings.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Georgian Mathematical Journal
Volume	12
Issue number	1
DOIs	https://doi.org/10.1515/GMJ.2005.1
Publication status	Published - 2005

Keywords

Cocoercive mapping
convergence of projection methods
relaxed cocoercive mapping
relaxed pseudococoercive variational inequality
two-step system of variational inequalities

Access to Document

10.1515/GMJ.2005.1

Cite this

@article{d6cea8f2a9004a0eae3c4c6f29767489,

title = "Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods",

abstract = "The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets of real Hilbert spaces H1 and H2, respectively. The two-step SNVI problem considered here is as follows: find an element (x*; y*) ∈ H1 × H2 such that (g(x*); g(y*)) ∈K1 × K2 and (formula omitted) are nonlinear mappings.",

keywords = "Cocoercive mapping, convergence of projection methods, relaxed cocoercive mapping, relaxed pseudococoercive variational inequality, two-step system of variational inequalities",

author = "Agarwal, {Ravi P.} and Donal O'Regan and Verma, {Ram U.}",

year = "2005",

doi = "10.1515/GMJ.2005.1",

language = "English",

volume = "12",

pages = "1--10",

journal = "Georgian Mathematical Journal",

issn = "1072-947X",

number = "1",

}

TY - JOUR

T1 - Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

AU - Agarwal, Ravi P.

AU - O'Regan, Donal

AU - Verma, Ram U.

PY - 2005

Y1 - 2005

N2 - The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets of real Hilbert spaces H1 and H2, respectively. The two-step SNVI problem considered here is as follows: find an element (x*; y*) ∈ H1 × H2 such that (g(x*); g(y*)) ∈K1 × K2 and (formula omitted) are nonlinear mappings.

AB - The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let K1 and K2 be nonempty closed convex subsets of real Hilbert spaces H1 and H2, respectively. The two-step SNVI problem considered here is as follows: find an element (x*; y*) ∈ H1 × H2 such that (g(x*); g(y*)) ∈K1 × K2 and (formula omitted) are nonlinear mappings.

KW - Cocoercive mapping

KW - convergence of projection methods

KW - relaxed cocoercive mapping

KW - relaxed pseudococoercive variational inequality

KW - two-step system of variational inequalities

UR - http://www.scopus.com/inward/record.url?scp=85025991998&partnerID=8YFLogxK

U2 - 10.1515/GMJ.2005.1

DO - 10.1515/GMJ.2005.1

M3 - Article

AN - SCOPUS:85025991998

SN - 1072-947X

VL - 12

SP - 1

EP - 10

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 1

ER -

Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this