Araştırma Makalesi
BibTex RIS Kaynak Göster

Existence Results for Systems of Quasi-Variational Relations

Yıl 2019, , 217 - 222, 01.12.2019
https://doi.org/10.33205/cma.643397

Öz

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. 

Kaynakça

  • [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.
Yıl 2019, , 217 - 222, 01.12.2019
https://doi.org/10.33205/cma.643397

Öz

Kaynakça

  • [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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Daniela Inoan 0000-0003-4666-1480

Yayımlanma Tarihi 1 Aralık 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA 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. Aralık 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, sy. 4 (Aralık 2019): 217-22. https://doi.org/10.33205/cma.643397.
EndNote Inoan D (01 Aralık 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, c. 2, sy. 4, ss. 217–222, 2019, doi: 10.33205/cma.643397.
ISNAD Inoan, Daniela. “Existence Results for Systems of Quasi-Variational Relations”. Constructive Mathematical Analysis 2/4 (Aralık 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, c. 2, sy. 4, 2019, ss. 217-22, doi:10.33205/cma.643397.
Vancouver Inoan D. Existence Results for Systems of Quasi-Variational Relations. CMA. 2019;2(4):217-22.