Existence Results for Systems of Quasi-Variational Relations

Year 2019, , 217 - 222, 01.12.2019

Daniela Inoan

https://doi.org/10.33205/cma.643397

Cited By: 1

Abstract

We study the existence of solutions for a  system of variational relations, in a general form, using a fixed point result for contractions in metric spaces. As a particular case, we give sufficient conditions for the existence of solutions of a system of quasi-equilibrium problems. 

Keywords

variational relations, systems of equilibrium problems

References

• [1] R. P. Agarwal, M. Balaj and D. O’Regan: Variational relation problems in a general setting. Journal of Fixed Point Theory and Applications 18 (2016), 479–493.
• [2] M. Balaj: Systems of variational relations with lower semicontinuous set-valued mappings. Carpathian Journal of Mathematics 31 (2015), 269–275.
• [3] A. Granas and J. Dugundji: Fixed Point Theory, Springer-Verlag, Berlin, 2003.
• [4] D. Inoan: Variational relations problems via fixed points of contraction mappings. Journal of Fixed Point Theory and Applications 19 (2017), 1571–1580.
• [5] D. Inoan: Factorization of quasi-variational relations systems. Acta Mathematica Vietnamica 39 (2014), 359-365.
• [6] G. Kassay, J. Kolumbán and Z. Páles: Factorization of Minty and Stampacchia variational inequality systems. European J. Oper. Res. 143 (2002), 377-389.
• [7] A. Latif and D. T. Luc: Variational relation problems: existence of solutions and fixed points of contraction mappings. Fixed Point Theory and Applications (2013) Article id. 315, 1–10.
• [8] L-J. Lin and Q. H. Ansari: Systems of quasi-variational relations with applications. Nonlinear Anal. 72 (2010), 1210– 1220.
• [9] L-J. Lin, M. Balaj and Y. C. Ye: Quasi-variational relation problems and generalized Ekeland’s variational principle with applications. Optimization 63 (2014), 1353–1365.
• [10] L-J. Lin and S-Y. Wang: Simultaneous variational relation problems and related applications. Computers and Mathematics with Applications 58 (2009), 1711–1721.
• [11] D. T. Luc: An abstract problem in variational analysis. J. Optim. Theory Appl. 138 (2008), 65–76.
• [12] Y. J. Pu and Z. Yang: Variational relation problem without the KKM property with applications. J. Math. Anal. Appl. 393 (2012), 256–264.
• [13] S. Reich: Fixed point of contractive functions. Boll. Un. Mat. Ital. 5 (1972), 26-42.
• [14] I. A. Rus, A. Petrusel and G. Petrusel: Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.