Skip to main content
SpringerLink
Log in

Maximal elements of a family of G B-majorized mappings in product FC-spaces and applications

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A new family of G B-majorized mappings from a topological space into a finite continuous topological spaces (in short, FC-space) involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of G B-majorized mappings are proved under noncompact setting of product FC-spaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ding Xieping. Maximal element theorems in product FC-spaces and generalized games[J]. J Math Anal Appl, 2005, 305(1):29–42.

    Article  MathSciNet  Google Scholar 

  2. Lassonde M. On the use of KKM multifunctions in fixed point theory and related topics[J]. J Math Anal Appl, 1983, 97(1):151–201.

    Article  MathSciNet  Google Scholar 

  3. Horvath C D. Contractibility and general convexity[J]. J Math Anal Appl, 1991, 156(2):341–357.

    Article  MathSciNet  Google Scholar 

  4. Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J]. J Math Anal Appl, 1997, 209(3):551–571.

    Article  MathSciNet  Google Scholar 

  5. Ben-El-Mechaiekh H, Chebbi S, Florenzano M, Llinares J. Abstract convexity and fixed points[J]. J Math Anal Appl, 1998, 222(1):138–151.

    Article  MathSciNet  Google Scholar 

  6. Ding Xieping. Maximal element principles on generalized convex spaces and their application[M]. In: Argawal R P (ed). Set Valued Mappings with Applications in Nonlinear Analysis, in: SIMMA, Vol. 4, 2002, 149–174.

  7. Ding Xieping. Maximal elements for G B-majorized mappings in product G-convex spaces and applications (I)[J]. Appl Math Mech (English Edition), 2003, 24(6):659–672.

    Article  MathSciNet  Google Scholar 

  8. Ding Xieping. Maximal elements for G B-majorized mappings in product G-convex spaces and applications (II)[J]. Appl Math Mech (English Edition), 2003, 24(9):1017–1034.

    MathSciNet  Google Scholar 

  9. Deguire P, Tan K K, Yuan X Z. The study of maximal elements, fixed points for L S-majorized mappings and their applications to minimax and variational inequalities in product topological spaces[J]. Nonlinear Anal, 1999, 37(7):933–951.

    Article  MathSciNet  Google Scholar 

  10. Shen Z F. Maximal element theorems of H-majorized correspondence and existence of equilibrium for abstract economies[J]. J Math Anal Appl, 2001, 256(1):67–79.

    Article  MathSciNet  Google Scholar 

  11. Dugundji J. Topology[M]. Allyn and Bacon, Boston, 1966.

    Google Scholar 

  12. Aubin J P, Ekeland I. Applied Nonlinear Analysis[M]. John Wiley & Sons, New York, 1984.

    Google Scholar 

  13. Yannelis N C, Prabhakar N D. Existence of maximal elements and equilibria in linear topological spaces[J]. J Math Econom, 1983, 12(3):233–245.

    Article  MathSciNet  Google Scholar 

  14. Ding Xieping, Tan K K. On equilibria of noncompact generalized games[J]. J Math Anal Appl, 1993, 177(1):226–238.

    Article  MathSciNet  Google Scholar 

  15. Ding Xieping, Kim W K, Tan K K. Equilibria of generalized games with L-majorized correspondences[J]. Internat J Math Math Sci, 1994, 17(4):783–790.

    Article  MathSciNet  Google Scholar 

  16. Tulcea C I. On the Equilibriums of Generalized Games[R]. The Center for Math. Studies in Economics and Management Science, paper No. 696, 1986.

  17. Toussaint S. On the existence of equilibria in economies with infinite commodities and without ordered preferences[J]. J Econom Theory, 1984, 33(1):98–115.

    Article  MathSciNet  Google Scholar 

  18. Borglin A, Keiding, H. Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems[J]. J Math Econom, 1976, 3(3):313–316.

    Article  MathSciNet  Google Scholar 

  19. Ding Xieping. Fixed points, minimax inequalities and equilibria of noncompact generalized games[J]. Taiwanese J Math, 1998, 2(1):25–55.

    MathSciNet  Google Scholar 

  20. Ding Xieping, Yuan G X-Z. The study of existence of equilibria for generalized games without lower semicontinuity in locally convex topological vector spaces[J]. J Math Anal Appl, 1998, 227(2):420–438.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P. R. China

    Ding Xie-ping  (丁协平) (Professor)

Authors
  1. Ding Xie-ping  (丁协平)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ding Xie-ping  (丁协平).

Additional information

Contributed by DING Xie-ping

Project supported by the Natural Science Foundation of Sichuan Education Department of China (Nos.2003A081 and SZD0406)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, Xp. Maximal elements of a family of G B-majorized mappings in product FC-spaces and applications. Appl Math Mech 27, 1607–1618 (2006). https://doi.org/10.1007/s10483-006-1203-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-1203-1

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation