Abstract
Using a fixed point result of the author we establish a variety of new collectively coincidence point results between different classes of multivalued maps.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of Data and Materials
Not applicable.
References
Agarwal, R.P., O’Regan, D., Park, S.: Fixed point theory for multimaps in extension type spaces. J. Korean Math. Soc. 39, 579–591 (2002)
Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis. Springer, Berlin (1994)
Ben-El-Mechaiekh, H., Deguire, P., Granas, A.: Points fixes et coincidences pour les applications multivoques II (applications de type \(\Phi \) and \(\Phi ^{\star }\)). C. R. Acad. Sci. 295, 381–384 (1982)
Deguire, P., Lassonde, M.: Familles sélectantes. Topol. Methods Nonlinear Anal. 5, 261–269 (1995)
Engelking, R.: General Topology. Heldermann Verlag, Berlin (1989)
Gorniewicz, L.: Topological Fixed Point Theory of Multivalued Mappings. Kluwer Academic Publishers, Dordrecht (1991)
Lim, L.J., Park, S., Yu, Z.T.: Remarks on fixed points, maximal elements and equilibria of generalized games. J. Math. Anal. Appl. 233, 581–596 (1999)
O’Regan, D.: Fixed point theory for extension type spaces and essential maps on topological spaces. Fixed Point Theory Appl. 1, 13–20 (2004)
O’Regan, D.: Deterministic and random fixed points for maps on extension type spaces. Appl. Anal. 97, 1960–1966 (2018)
O’Regan, D.: Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps. Topol. Appl. 284, Art. No. 107368 (2020)
O’Regan, D.: Maximal type elements for families. Symmetry 13(12), paper No. 2269 (2021)
O’Regan, D.: Collectively coincidence type results and applications. Appl. Anal. 102, 890–901 (2023)
Yanelis, N.C., Prabhakar, N.D.: Existence of maximal elements and equlibria in linear topological spaces. J. Math. Econom. 12, 233–245 (1983)
Yuan, X.Z.: The study of minimax inequalities and applications to economies and variational inequalities. Mem. AMS 132(625) (1998)
Yuan, X.Z.: The study of equilibria for abstract economies in topological vector spaces—a unified approach. Nonlinear Anal. 37, 409–430 (1999)
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
Not applicable.
Corresponding author
Ethics declarations
Conflict of interest
The author declares no conflict of interest.
Ethical approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
About this article
Cite this article
O’Regan, D. Selecting Families and Coincidence Theory. Results Math 78, 227 (2023). https://doi.org/10.1007/s00025-023-02006-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-023-02006-1