New existence criteria of the solutions for a variational relation problem. (4th May 2017)

• Record Type: Journal Article
• Authors: Balaj, Mircea
• Is Part Of: Optimization. Volume 66:Number 5(2017)
• Page Start: 675
• Page End: 689
• Publication Date: 2017-05-04
• Subjects: Variational relation problem -- fixed point -- continuous selection -- quasiequilibrium problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1296836
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Many quasivariational inclusions or quasiequilibrium problems, encountered in the literature, are special cases of a variational relation problem proposed in a recent paper by Agarwal et al. (J. Optim. Theory Appl. 2012;155:417–429). The purpose of this paper is to establish new existence results for the solutions of this problem. The main ingredients in the proofs are some continuous selection and fixed point theorems, and an interesting section result. In the last section, we prove that, applied for some concrete relations, our results are different from those obtained by other authors.