Skip to main content
Log in

Intersection results for general classes of maps

  • Original Research
  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper we use new coincidence theorems of the author to obtain a variety of Ky Fan matching type theorems for open coverings related to the map or maps. To establish our new matching results, we consider maps which are of KKM or BPK type (these include the Kakutani maps, the acyclic maps and more generally the admissible maps of Gorniewicz) together with maps which generate HLPY type maps.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Data availability

Not Applicable.

References

  1. C.D. Aliprantis and K.C. Border, Infinite dimensional analysis, Springer Verlag, Berlin, 1994.

    Book  Google Scholar 

  2. H. Ben-El-Mechaiekh, P. Deguire and A. Granas, Points fixes et coincidences pour les applications multivoques II (Applications de type \(\Phi \) and \(\Phi ^{\star }\)), C.R. Acad. Sc.295(1982), 381–384.

  3. T.H. Chang, Y.Y. Huang, J.C. Jeng and T.H. Chang and K.H. Kuo, On \(S\)–KKM property and related topics, Jour. Math. Anal. Appl., 229(1999), 212–227.

  4. T.H. Chang and C.L. Yen, KKM property and fixed point theorems, Jour. Math. Anal. Appl., 203(1996), 224–235.

    Article  MathSciNet  Google Scholar 

  5. X.P. Ding, W.K. Kim and K.K. Tan, A selection theorem and its applications, Bulletin Australian Math. Soc., 46(1992), 205–212.

    Article  MathSciNet  Google Scholar 

  6. L. Gorniewicz, Topological fixed point theory of multivalued mappings, Kluwer Acad. Publishers, Dordrecht, 1991.

    Google Scholar 

  7. L. Gorniewicz and M. Slosarski, Topological essentiality and differential inclusions, Bull. Austral. Math. Soc., 45(1992), 177–193.

    Article  MathSciNet  Google Scholar 

  8. L.J. Lim, S. Park and Z.T. Yu, Remarks on fixed points, maximal elements and equilibria of generalized games, Jour. Math. Anal. Appl., 233(1999), 581–596.

    Article  MathSciNet  Google Scholar 

  9. D. O’Regan, Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps, Topology and its Applications, 284(2020), Art. No. 107368, 6pp.

  10. D. O’Regan, KKM type maps and collectively coincidence theory, submitted.

  11. D. O’Regan, Coincidence theory for better admissible multifunctions, Journal of Analysis, to appear.

  12. D.O’Regan and J. Peran, Fixed points for better admissible multifunctions on proximity spaces, Jour. Math. Anal. Appl., 380(2011), 882–887.

    Article  MathSciNet  Google Scholar 

  13. S. Park, Coincidence theorems for the better admissible multimaps and their applications, Nonlinear Anal. , 30(1997), 4183–4191.

    Article  MathSciNet  Google Scholar 

  14. N.C. Yanelis and N.D. Prabhakar, Existence of maximal elements and equlibria in linear topological spaces, J. Math. Econom., 12(1983), 233–245.

    Article  MathSciNet  Google Scholar 

Download references

Funding

Not Applicable.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Donal O’Regan.

Ethics declarations

Competing Interests

The author declares no conflict of interest.

Ethical Approval

Not Applicable.

Additional information

Communicated by B V Rajarama Bhat.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

O’Regan, D. Intersection results for general classes of maps. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00559-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13226-024-00559-7

Keywords

Mathematics Subject Classification

Navigation