Coincidence theory and maps with an inclusion property
DOI:
https://doi.org/10.56754/0719-0646.2803.545Keywords:
Coincidence points, fixed points, set-valued mapsAbstract
In this paper we consider a class of maps (whose convex hull has a nice selection property) with another general class of maps and we present coincidence results between these two classes.
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References
[1] C. D. Aliprantis and K. C. Border, Infinite dimensional analysis. A hitchhiker’s guide, ser. Stud. Econ. Theory. Berlin: Springer-Verlag, 1994, vol. 4.
[2] H. Bel-El-Mechaiekh, P. Deguire, and A. Granas, “Fixed points and coincidences for set-valued maps. II: Maps of type φ and φ*,” C. R. Acad. Sci., Paris, Sér. I, vol. 295, pp. 381–384, 1982.
[3] H. Ben-El-Mechaiekh and P. Deguire, “Approachability and fixed points for non-convex set-valued maps,” J. Math. Anal. Appl., vol. 170, no. 2, pp. 477–500, 1992, doi: 10.1016/0022-247X(92)90032-9.
[4] T.-H. Chang, Y.-Y. Huang, and J.-C. Jeng, “Fixed-point theorems for multifunctions in S-KKM class,” Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, vol. 44, no. 8, pp. 1007–1017, 2001, doi: 10.1016/S0362-546X(99)00318-1.
[5] T.-H. Chang and C.-L. Yen, “KKM property and fixed point theorems,” J. Math. Anal. Appl., vol. 203, no. 1, pp. 224–235, 1996, doi: 10.1006/jmaa.1996.0376.
[6] P. Deguire and M. Lassonde, “Selecting families,” Topol. Methods Nonlinear Anal., vol. 5, no. 2, pp. 261–269, 1995, doi: 10.12775/TMNA.1995.017.
[7] X. P. Ding, W. K. Kim, and K.-K. Tan, “A selection theorem and its applications,” Bull. Aust. Math. Soc., vol. 46, no. 2, pp. 205–212, 1992.
[8] R. Engelking, General topology., ser. Sigma Ser. Pure Math. Berlin: Heldermann Verlag, 1989, vol. 6.
[9] L. Górniewicz, Topological fixed point theory of multivalued mappings, ser. Math. Appl. Dordrecht: Kluwer Academic Publishers, 1999, vol. 495.
[10] W. He and N. C. Yannelis, “Equilibria with discontinuous preferences: new fixed point theorems,” J. Math. Anal. Appl., vol. 450, no. 2, pp. 1421–1433, 2017, doi: 10.1016/j.jmaa.2017.01.089.
[11] C. D. Horvath, “Contractibility and generalized convexity,” J. Math. Anal. Appl., vol. 156, no. 2, pp. 341–357, 1991, doi: 10.1016/0022-247X(91)90402-L.
[12] M. A. Khan, R. P. McLean, and M. Uyanik, “On equilibria in constrained generalized games with the weak continuous inclusion property,” J. Math. Anal. Appl., vol. 537, no. 1, 2024, Art. ID 128258, doi: 10.1016/j.jmaa.2024.128258.
[13] L.-J. Lin, S. Park, and Z.-T. Yu, “Remarks on fixed points, maximal elements, and equilibria of generalized games,” J. Math. Anal. Appl., vol. 233, no. 2, pp. 581–596, 1999, doi: 10.1006/jmaa.1999.6311.
[14] D. O’Regan, “Wu maps and collectively coincidence theory,” Acta Math. Hung., vol. 175, no. 2, pp. 472–485, 2025, doi: 10.1007/s10474-025-01530-6.
[15] D. O’Regan, “Fixed point theory on extension-type spaces and essential maps on topological spaces,” Fixed Point Theory Appl., vol. 2004, no. 1, pp. 13–20, 2004, doi: 10.1155/S1687182004311046.
[16] D. O’Regan, “Deterministic and random fixed points for maps on extension type spaces,” Appl. Anal., vol. 97, no. 11, pp. 1960–1966, 2018, doi: 10.1080/00036811.2017.1344228.
[17] D. O’Regan, “Continuous selections and collectively fixed point theory with applications to generalized games,” Aequationes Math., vol. 97, no. 3, pp. 619–628, 2023, doi: 10.1007/s00010-022-00921-2.
[18] D. O’Regan, “KKM type maps and collectively coincidence theory,” Constr. Math. Anal., vol. 8, no. 4, pp. 176–186, 2025, doi: 10.33205/cma.1769838.
[19] S. Park, “Coincidence theorems for the better admissible multimaps and their applications,” Nonlinear Anal., Theory Methods Appl., vol. 30, no. 7, pp. 4183–4191, 1997, doi: 10.1016/S0362-546X(97)00385-4.
[20] S. Park, “A unified fixed point theory of multimaps on topological vector spaces,” J. Korean Math. Soc., vol. 35, no. 4, pp. 803–829, 1998.
[21] N. C. Yannelis and N. Prabhakar, “Existence of maximal elements and equilibria in linear topological spaces,” J. Math. Econ., vol. 12, no. 3, pp. 233–245, 1983, doi: 10.1016/0304-4068(83)90041-1.
[22] G. X.-Z. Yuan, The study of minimax inequalities and applications to economies and variational inequalities, ser. Mem. Am. Math. Soc. Providence, RI: American Mathematical Society (AMS), 1998, vol. 625, doi: 10.1090/memo/0625.
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