Skip to main content
SpringerLink
Log in

Fixed Points, Coincidence Equations on Cones and Complementarity

  • Chapter
Topological Methods in Complementarity Theory

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 41))

  • 389 Accesses

Abstract

A well-known fact, in complementarity theory is the relation between the complementarity condition and the notions of fixed point or the notion of p tY coincidence point.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  • ALTMAN, M. 1. A fixed point theorem in Hilbert spaces. Bull. Acad. Polon. Sci. 5 (1957), 19–22

    MathSciNet  MATH  Google Scholar 

  • BANAS, J. and GOEBEL, K. 1. Measure of Noncompactness in Banach Spaces. Lecture Notes in Pure and Appl. Math. Vol. 60, Marcel Dekker Inc., New York and Basel (1980).

    Google Scholar 

  • BOD, P. 1. On closed sets having a least element. In: Lecture Notes in Econom. and Math. System, 117, Springer-Verlag (1976), 23–34.

    Google Scholar 

  • BOD, P. 2. Sur un model non-linéarire de rapports interindustriels. Rairo Rech. Opér. 11 (1977), 405–415.

    MathSciNet  MATH  Google Scholar 

  • BOYD, D. W. and WONG, J. S. W. 1. A nonlinear contraction. Proc. Amer. Math. Soc. 20 (1969), 458–464.

    Article  MathSciNet  MATH  Google Scholar 

  • BROWDER, F. E. 1. Non-expansive non-linear operators in Banach spaces. Proc. Nat. Acad. Sci. Usa 54 (1965), 1041–1044.

    Article  MathSciNet  MATH  Google Scholar 

  • DESBIENS, J. 1. Méthode de Mann et calcul des points fixes des applications multivoques dans les espaces de Banach. Ann. Sci. Math. Québec, 12 Nr. 1 (1988), 5–30.

    MathSciNet  MATH  Google Scholar 

  • DUGUNDJI, F. and GRANAS, A 1. Fixed Point Theory. Warszawa (1982).

    MATH  Google Scholar 

  • FUJIMOTO, T. 1. Nonlinear complementarity problems in function spaces. Siam J. Control Opt., 18 (1980), 621–623.

    Article  MathSciNet  MATH  Google Scholar 

  • FUJIMOTO, T. 2. An extension of Tarski ‘s fixed point theorem and its application to isotone complementarity problems. Math. Programming 28 (1984), 116–118.

    Article  MathSciNet  MATH  Google Scholar 

  • GUO, D. and LAKSHMIKANTAHATM, V. 1. Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. Theory, Meth. Appl. 11 Nr. 5 (1987), 623–632.

    Article  MATH  Google Scholar 

  • ISAC, G. 1. Un théorème de point fixe. Application à la comparaison des equations différentielles dans les espaces deBanach ordonnés. Libertas Mathematica 1, (1981), 75–80.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. 2. On the implicit complementarity problem in Hilbert spaces. Bull. Australian Math. Soc., 32 Nr. 2 (1985), 251–260.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 3. Complementarity problem and coincidence equations on convex cones. Boll. Unione Mat. Ital. (6), 5-B (1986), 925–943.

    MathSciNet  Google Scholar 

  • ISAC, G. 4. Fixed point theory, coincidence equations on convex cones and complementarity problem. Contemporary Math., Vol. 72 (1988), 139–155.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 5. Fixed point theory and complementarity problem in Hilbert spaces. Bull. Australian Math. Soc., 36 Nr.2 (1987), 295–310.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. 6. Iterative methods for the general order complementarity problem. In: S. P. Singh (Ed.), Approximation Theory, Spline Functions and Applications, Kluwer (1992), 365–380.

    Google Scholar 

  • ISAC, G. 7. Tihonov’s regularization and the complementarity problem in Hilbert spaces. J. Math. Anal. Appl. 174 Nr.1 (1993). 53–66.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. 8. On an Altman type fixed point theorem on convex cones. Rocky Mountain, J. Math. 25 Nr. 2 (1995) 701–714.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. 9. Fixed point theorems on convex cones, generalized pseudo-contractive mappings and the complementarity problem. Bull. Institute Math. Acad. Sinica, 23 Nr. 1 (1995), 21–35.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. 10. A generalization of Karamardian ‘s condition in complementarity theory. Nonlinear Analysis Forum, 4 (1999), 49–63.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. and GOELEVEN, D. 1. Existence theorems for the implicit complementarity problem. Internat. J. Math. & Math. Sci. Vol. 16 Nr. 1 (1993), 67–74.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and Goeleven, D. 2. The implicit general order complementarity problem, models and iterative methods. Annals Oper. Research, 44 (1993), 63–92.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and KOSTREVA, M. 1. The generalized order complementarity problem. J. Opt. Theory Appl., Nr. 3 (1991), 517–534.

    Article  MathSciNet  Google Scholar 

  • ISAC, G. and Kostreva, M. 2. Kneser’s theorem and the multivalued generalized order complementarity problem. Appl. Math. Lett. Vol. 4 Nr. 6, (1991), 81–85.

    Article  MathSciNet  MATH  Google Scholar 

  • ISAC, G. and Kostreva, M. 3. The implicity generalized order complementarity problem and Leontief’s input-output model. Applicationes Mathematical 24 Nr. 2 (1996), 113–125.

    MathSciNet  MATH  Google Scholar 

  • ISAC, G. and Németh, A. B 1. Isotone projection cones in Hilbert spaces and the complementarity problem. Bolletino, U. M Ital., (7)4-B (1990), 773–802.

    Google Scholar 

  • ISAC, G. and Németh, A. B 2. Projection methods, isotone projection cones and the complementarity problem. J. Math. Anal. Appl. 153, Nr. 1 (1990), 258–275.

    Article  MathSciNet  MATH  Google Scholar 

  • ISHIKAWA, S. 1. Fixed points and iterations of a nonexpansive mapping in a Banach space. Proc. Amer. Math. Soc. 59 Nr. 1 (1976), 65–71.

    Article  MathSciNet  MATH  Google Scholar 

  • JACHYMSKI, J. 1. On Isac’s fixed point theorem for selfmaps of a Galerkin cone. Ann Sci. Math. Québec, 18 Nr.2 (1994), 169–171.

    MathSciNet  MATH  Google Scholar 

  • KNESER, H. 1. Ein directe Ableitung des Zornschen Lemas aus demn Auswahlaxiom. Mathmatische Zeitschrift. 53 (1950), 110–113.

    Article  MathSciNet  MATH  Google Scholar 

  • KRANSNOSELSKII, M. A. 1. Positive Solutions of Operator Equations. Noordhoff, Groningen, (1964).

    Google Scholar 

  • LIONS, J. L. and STAMPACCHIA, G. 1. Variational inequalities,. Comm. Pure Appl. Math. 20 (1967), 493–519.

    Article  MathSciNet  MATH  Google Scholar 

  • MANN, W. R. 1. Mean valued methods in iteration. Proc. Amer. Math. Soc., 4(1953), 506–510.

    Article  MathSciNet  MATH  Google Scholar 

  • OPOITSEV, V. I. 1. A generalization of the theory of monotone and concave operators. Trans. Moscow, Math. Soc. Nr. 2 (1979), 243–279.

    Google Scholar 

  • POTTER, A. J. B. 1. Applications of Hilbert’s projective metric to certain classes of nonhomogeneous operators. Quart.J. Math., Oxford Ser. (2) 28 (1977), 93–99.

    Article  MathSciNet  MATH  Google Scholar 

  • SADOVSKI, B. N. 1. A fized point principle. Funktsional Anal. i Prilozhen, 1 (1967), 74–76.

    Google Scholar 

  • SUBRAMANIAN, P. K. 1. A dual exact penalty linear complementarity problem. J. Optim. Theory Appl. 58 Nr. 3 (1988), 525–538.

    Article  MathSciNet  MATH  Google Scholar 

  • SUBRAMANIAN, P. K. 2. A note on least two norm solutions of monotone complementarity problems. App. Math. Lett. 1 Nr. 4 (1988), 395–397.

    Article  MATH  Google Scholar 

  • TAMIR, A. 1. Minimality and complementarity properties associated with Z-functions and M-functions. Math. Programming 7 (1974), 17–31.

    Article  MathSciNet  MATH  Google Scholar 

  • TARSKI, A. 1. A lattice-theoretical fixed point theorem and its applications. Pacific J. Mathematics, 5 (1955), 285–309.

    Article  MathSciNet  MATH  Google Scholar 

  • THOMPSON, A. C. 1. On certain contraction mappings in a partially ordered vector space. Proc. Amer. Math. Soc. 14 Nr.3 (1963), 438–443 .

    MathSciNet  MATH  Google Scholar 

  • ZEIDLER, E. 1. Nonlinear Functional Analysis and its Applications. Vol. I, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, (1985).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada

    George Isac

Authors
  1. George Isac
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Isac, G. (2000). Fixed Points, Coincidence Equations on Cones and Complementarity. In: Topological Methods in Complementarity Theory. Nonconvex Optimization and Its Applications, vol 41. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3141-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3141-5_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4828-1

  • Online ISBN: 978-1-4757-3141-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation