Research Article
BibTex RIS Cite

KKM type maps and collectively coincidence theory

Year 2025, Volume: 8 Issue: 4, 176 - 186, 15.12.2025
https://doi.org/10.33205/cma.1769838

Abstract

In this paper, we present some properties of KKM maps and then use them to obtain a variety of collectively coincidence results for multivalued maps.

References

  • C. D. Aliprantis, K. C. Border: Infinite dimensional analysis, Springer Verlag, Berlin (1994).
  • H. Ben-El-Mechaiekh, P. Deguire and A. Granas: Points fixes et coincidences pour les applications multivoques II (Applications de type Φ and Φ⋆), C.R. Acad. Sc., 295 (1982), 381–384.
  • T. H. Chang, Y. Y. Huang, J. C. Jeng, T. H. Chang and K. H. Kuo: On S–KKM property and related topics, J. Math. Anal. Appl., 229 (1999), 212–227.
  • T. H. Chang, Y. Y. Huang and J. C. Jeng: Fixed point theorems for multifunctions in S–KKM class, Nonlinear Anal., 44 (2001), 1007–1017.
  • T. H. Chang, C. L. Yen: KKM property and fixed point theorems, J. Math. Anal. Appl., 203 (1996), 224–235.
  • P. Deguire, M. Lassonde: Familles sélectantes, Topological Methods in Nonlinear Anal., 5 (1995), 261–269.
  • X. P. Ding, W. K. Kim and K. K. Tan: A selection theorem and its applications, Bulletin Australian Math. Soc., 46 (1992), 205–212.
  • R. Engelking: General Topology, Heldermann Verlag, Berlin (1989).
  • L. Gorniewicz: Topological fixed point theory of multivalued mappings, Kluwer Acad. Publishers, Dordrecht (1991).
  • L. J. Lin, S. Park and Z. T. Yu: Remarks on fixed points, maximal elements and equilibria of generalized games, J. Math. Anal. Appl., 233 (1999), 581–596.
  • L. J. Lin, Z. T. Yu: Fixed point theorems of KKM-type maps, Nonlinear Anal., 38 (1999), 265–275.
  • D. O’Regan: Fixed point theory for extension type spaces and essential maps on topological spaces, Fixed Point Theory Appl., 1 (2004), 13–20.
  • D. O’Regan: Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps, Topology Appl., 284 (2020), Article ID: 107368.
  • D. O’Regan: Selecting families and coincidence theory, Results Math., 78 (2023), Article ID: 227.
  • N.C. Yanelis, N. D. Prabhakar: Existence of maximal elements and equlibria in linear topological spaces, J. Math. Econom., 12 (1983), 233–245.
  • X. Z. Yuan: The study of minimax inequalities and applications to economies and variational inequalities, Memoirs of the AMS, 132 (625), American Mathematical Society, Rhode Island (1998).
There are 16 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Donal O'regan 0000-0002-4096-1469

Submission Date August 21, 2025
Acceptance Date December 3, 2025
Early Pub Date December 9, 2025
Publication Date December 15, 2025
Published in Issue Year 2025 Volume: 8 Issue: 4

Cite

APA O’regan, D. (2025). KKM type maps and collectively coincidence theory. Constructive Mathematical Analysis, 8(4), 176-186. https://doi.org/10.33205/cma.1769838
AMA O’regan D. KKM type maps and collectively coincidence theory. CMA. December 2025;8(4):176-186. doi:10.33205/cma.1769838
Chicago O’regan, Donal. “KKM Type Maps and Collectively Coincidence Theory”. Constructive Mathematical Analysis 8, no. 4 (December 2025): 176-86. https://doi.org/10.33205/cma.1769838.
EndNote O’regan D (December 1, 2025) KKM type maps and collectively coincidence theory. Constructive Mathematical Analysis 8 4 176–186.
IEEE D. O’regan, “KKM type maps and collectively coincidence theory”, CMA, vol. 8, no. 4, pp. 176–186, 2025, doi: 10.33205/cma.1769838.
ISNAD O’regan, Donal. “KKM Type Maps and Collectively Coincidence Theory”. Constructive Mathematical Analysis 8/4 (December2025), 176-186. https://doi.org/10.33205/cma.1769838.
JAMA O’regan D. KKM type maps and collectively coincidence theory. CMA. 2025;8:176–186.
MLA O’regan, Donal. “KKM Type Maps and Collectively Coincidence Theory”. Constructive Mathematical Analysis, vol. 8, no. 4, 2025, pp. 176-8, doi:10.33205/cma.1769838.
Vancouver O’regan D. KKM type maps and collectively coincidence theory. CMA. 2025;8(4):176-8.