Araştırma Makalesi
BibTex RIS Kaynak Göster

Remarks on saddle points of vector-valued functions

Yıl 2022, , 72 - 77, 31.03.2022
https://doi.org/10.53006/rna.1086597

Öz

Using a coincidence theorem for multimaps, we prove the existence of a saddle point for vector-valued functions in topological vector spaces by means of scalarized maps.
Moreover, we discuss minimax theorems as a consequence of the saddle point theorem for real-valued functions.

Kaynakça

  • [1] S.-S. Chang, X.-Z. Yuan, G.-M. Lee, and X.-L. Zhang, Saddle points and minimax theorems for vector-valued multifunctions on H-spaces, Appl. Math. Lett. 11 (1998) 101–107.
  • [2] F. Ferro, A minimax theorem for vector-valued functions, J. Optim. Theory Appl. 60 (1989) 19–31.
  • [3] F. Ferro, A minimax theorem for vector-valued functions, part 2, J. Optim. Theory Appl. 68 (1991) 35–48.
  • [4] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980) 73–77.
  • [5] I.-S. Kim, Saddle points of vector-valued functions in topological vector spaces, J. Korean Math. Soc. 37 (2000) 849–856.
  • [6] I.-S. Kim and Y.-T. Kim, Loose saddle points of set-valued maps in topological vector spaces, Appl. Math. Lett. 12 (1999) 21–26.
  • [7] I.-S. Kim and S. Park, Saddle point theorems on generalized convex spaces, J. Inequal. Appl. 5 (2000) 397–405.
  • [8] H. Komiya, Coincidence theorem and saddle point theorem, Proc. Amer. Math. Soc. 96 (1986) 599–602.
  • [9] D.T. Luc and C. Vargas, A saddle point theorem for set-valued maps, Nonlinear Anal. 18 (1992) 1–7.
  • [10] J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928) 295–320.
  • [11] J.W. Nieuwenhuis, Some minimax theorems in vector-valued functions, J. Optim. Theory Appl. 40 (1983) 463–475.
  • [12] S. Park and I.-S. Kim, Coincidence and saddle point theorems on generalized convex spaces, Bull. Korean Math. Soc. 37 (2000) 11–19.
  • [13] S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173–187.
  • [14] D.S. Shi and C. Ling, Minimax theorems and cone saddle points of uniformly same-order vector-valued functions, J. Optim. Theory Appl. 84 (1995) 575–587.
  • [15] K.-K. Tan, J. Yu, and X.-Z. Yuan, Existence theorems for saddle points of vector-valued maps, J. Optim. Theory Appl. 89 (1996) 731–747.
  • [16] T. Tanaka, Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces, J. Optim. Theory Appl. 62 (1989) 127–138.
  • [17] T. Tanaka, Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions, J. Optim. Theory Appl. 81 (1994) 355–377.
  • [18] E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer, New York, 1986.
Yıl 2022, , 72 - 77, 31.03.2022
https://doi.org/10.53006/rna.1086597

Öz

Kaynakça

  • [1] S.-S. Chang, X.-Z. Yuan, G.-M. Lee, and X.-L. Zhang, Saddle points and minimax theorems for vector-valued multifunctions on H-spaces, Appl. Math. Lett. 11 (1998) 101–107.
  • [2] F. Ferro, A minimax theorem for vector-valued functions, J. Optim. Theory Appl. 60 (1989) 19–31.
  • [3] F. Ferro, A minimax theorem for vector-valued functions, part 2, J. Optim. Theory Appl. 68 (1991) 35–48.
  • [4] C.-W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980) 73–77.
  • [5] I.-S. Kim, Saddle points of vector-valued functions in topological vector spaces, J. Korean Math. Soc. 37 (2000) 849–856.
  • [6] I.-S. Kim and Y.-T. Kim, Loose saddle points of set-valued maps in topological vector spaces, Appl. Math. Lett. 12 (1999) 21–26.
  • [7] I.-S. Kim and S. Park, Saddle point theorems on generalized convex spaces, J. Inequal. Appl. 5 (2000) 397–405.
  • [8] H. Komiya, Coincidence theorem and saddle point theorem, Proc. Amer. Math. Soc. 96 (1986) 599–602.
  • [9] D.T. Luc and C. Vargas, A saddle point theorem for set-valued maps, Nonlinear Anal. 18 (1992) 1–7.
  • [10] J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928) 295–320.
  • [11] J.W. Nieuwenhuis, Some minimax theorems in vector-valued functions, J. Optim. Theory Appl. 40 (1983) 463–475.
  • [12] S. Park and I.-S. Kim, Coincidence and saddle point theorems on generalized convex spaces, Bull. Korean Math. Soc. 37 (2000) 11–19.
  • [13] S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173–187.
  • [14] D.S. Shi and C. Ling, Minimax theorems and cone saddle points of uniformly same-order vector-valued functions, J. Optim. Theory Appl. 84 (1995) 575–587.
  • [15] K.-K. Tan, J. Yu, and X.-Z. Yuan, Existence theorems for saddle points of vector-valued maps, J. Optim. Theory Appl. 89 (1996) 731–747.
  • [16] T. Tanaka, Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces, J. Optim. Theory Appl. 62 (1989) 127–138.
  • [17] T. Tanaka, Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions, J. Optim. Theory Appl. 81 (1994) 355–377.
  • [18] E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer, New York, 1986.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

In-sook Kim Bu kişi benim

Yayımlanma Tarihi 31 Mart 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Kim, I.-s. (2022). Remarks on saddle points of vector-valued functions. Results in Nonlinear Analysis, 5(1), 72-77. https://doi.org/10.53006/rna.1086597
AMA Kim Is. Remarks on saddle points of vector-valued functions. RNA. Mart 2022;5(1):72-77. doi:10.53006/rna.1086597
Chicago Kim, In-sook. “Remarks on Saddle Points of Vector-Valued Functions”. Results in Nonlinear Analysis 5, sy. 1 (Mart 2022): 72-77. https://doi.org/10.53006/rna.1086597.
EndNote Kim I-s (01 Mart 2022) Remarks on saddle points of vector-valued functions. Results in Nonlinear Analysis 5 1 72–77.
IEEE I.-s. Kim, “Remarks on saddle points of vector-valued functions”, RNA, c. 5, sy. 1, ss. 72–77, 2022, doi: 10.53006/rna.1086597.
ISNAD Kim, In-sook. “Remarks on Saddle Points of Vector-Valued Functions”. Results in Nonlinear Analysis 5/1 (Mart 2022), 72-77. https://doi.org/10.53006/rna.1086597.
JAMA Kim I-s. Remarks on saddle points of vector-valued functions. RNA. 2022;5:72–77.
MLA Kim, In-sook. “Remarks on Saddle Points of Vector-Valued Functions”. Results in Nonlinear Analysis, c. 5, sy. 1, 2022, ss. 72-77, doi:10.53006/rna.1086597.
Vancouver Kim I-s. Remarks on saddle points of vector-valued functions. RNA. 2022;5(1):72-7.