Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems
Volume 11, Issue 3, pp 394416
http://dx.doi.org/10.22436/jnsa.011.03.08
Publication Date: February 16, 2018
Submission Date: November 10, 2017
Revision Date: January 03, 2018
Accteptance Date: January 11, 2018
Authors
LaiJiu Lin
 Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan.
Abstract
In this paper, we apply Theorem 3.2 of [G. M. Lee, L.J. Lin, J. Nonlinear Convex Anal., \({\bf 18}\) (2017), 17811800] to study
the variational inequality over split equality fixed point problems
for three finite families of strongly quasinonexpansive mappings.
Then we use this result to study variational inequalities over split
equality for three various finite families of nonlinear mappings. We
give a unified method to study split equality for three various
finite families of nonlinear problems. Our results contain many
results on split equality fixed point problems and multiple sets
split feasibility problems as special cases. Our results can treat
large scale of nonlinear problems by group these problems into
finite families of nonlinear problems, then we use simultaneous
iteration to find the solutions of these problems. Our results will
give a simple and quick method to study large scale of nonlinear
problems and will have many applications to study large scale of
nonlinear problems.
Share and Cite
ISRP Style
LaiJiu Lin, Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 3, 394416
AMA Style
Lin LaiJiu, Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems. J. Nonlinear Sci. Appl. (2018); 11(3):394416
Chicago/Turabian Style
Lin, LaiJiu. "Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems." Journal of Nonlinear Sciences and Applications, 11, no. 3 (2018): 394416
Keywords
 Split equality fixed point problem
 split fixed point problem
 quasipseudocontractive mapping
 demicontractive mapping
 pseudocontractive mapping
MSC
 47H06
 47H09
 47H10
 47J25
 65K15
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