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.
[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.
Year 2019,
Volume: 2 Issue: 4, 217 - 222, 01.12.2019
[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.
Inoan, D. (2019). Existence Results for Systems of Quasi-Variational Relations. Constructive Mathematical Analysis, 2(4), 217-222. https://doi.org/10.33205/cma.643397
AMA
Inoan D. Existence Results for Systems of Quasi-Variational Relations. CMA. December 2019;2(4):217-222. doi:10.33205/cma.643397
Chicago
Inoan, Daniela. “Existence Results for Systems of Quasi-Variational Relations”. Constructive Mathematical Analysis 2, no. 4 (December 2019): 217-22. https://doi.org/10.33205/cma.643397.
EndNote
Inoan D (December 1, 2019) Existence Results for Systems of Quasi-Variational Relations. Constructive Mathematical Analysis 2 4 217–222.
IEEE
D. Inoan, “Existence Results for Systems of Quasi-Variational Relations”, CMA, vol. 2, no. 4, pp. 217–222, 2019, doi: 10.33205/cma.643397.
ISNAD
Inoan, Daniela. “Existence Results for Systems of Quasi-Variational Relations”. Constructive Mathematical Analysis 2/4 (December 2019), 217-222. https://doi.org/10.33205/cma.643397.
JAMA
Inoan D. Existence Results for Systems of Quasi-Variational Relations. CMA. 2019;2:217–222.
MLA
Inoan, Daniela. “Existence Results for Systems of Quasi-Variational Relations”. Constructive Mathematical Analysis, vol. 2, no. 4, 2019, pp. 217-22, doi:10.33205/cma.643397.
Vancouver
Inoan D. Existence Results for Systems of Quasi-Variational Relations. CMA. 2019;2(4):217-22.