On the existence of ɛ-fixed points

Tiziana Cardinali

Open Mathematics (2014)

  • Volume: 12, Issue: 9, page 1320-1329
  • ISSN: 2391-5455

Abstract

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In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.

How to cite

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Tiziana Cardinali. "On the existence of ɛ-fixed points." Open Mathematics 12.9 (2014): 1320-1329. <http://eudml.org/doc/269167>.

@article{TizianaCardinali2014,
abstract = {In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.},
author = {Tiziana Cardinali},
journal = {Open Mathematics},
keywords = {Partially closed; β-w-partially closed; Weakly demiclosed; ɛ-fixed point; Fixed point; ɛ-Nash equilibrium; partially closed; $\beta $-$w$-partially closed; weakly demiclosed; -fixed point; fixed point; -Nash equilibrium},
language = {eng},
number = {9},
pages = {1320-1329},
title = {On the existence of ɛ-fixed points},
url = {http://eudml.org/doc/269167},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Tiziana Cardinali
TI - On the existence of ɛ-fixed points
JO - Open Mathematics
PY - 2014
VL - 12
IS - 9
SP - 1320
EP - 1329
AB - In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.
LA - eng
KW - Partially closed; β-w-partially closed; Weakly demiclosed; ɛ-fixed point; Fixed point; ɛ-Nash equilibrium; partially closed; $\beta $-$w$-partially closed; weakly demiclosed; -fixed point; fixed point; -Nash equilibrium
UR - http://eudml.org/doc/269167
ER -

References

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  1. [1] Brânzei R., Morgan J., Scalzo V., Tijs S., Approximate fixed point theorems in Banach spaces with applications in game theory, J. Math. Anal. Appl., 2003, 285(2), 619–628 http://dx.doi.org/10.1016/S0022-247X(03)00450-5 Zbl1037.47038
  2. [2] Chien S., Sinclair A., Convergence to approximate Nash equilibria in congestion games, In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, January 7–9, 2007, Society for Industrial and Applied Mathematics, Philadelphia, 2007, 169–178 Zbl1303.91018
  3. [3] Debreu G., A social equilibrium existence theorem, Proc. Nat. Acad. Sci. U.S.A., 1952, 38, 886–893 http://dx.doi.org/10.1073/pnas.38.10.886 Zbl0047.38804
  4. [4] Denkowski Z., Migórski S., Papageorgiou N.S., An Introduction to Nonlinear Analysis: Theory, Kluwer, Boston, 2003 
  5. [5] García-Falset J., Llorens-Fuster E., Suzuki T., Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl., 2011, 375(1), 185–195 http://dx.doi.org/10.1016/j.jmaa.2010.08.069 Zbl1214.47047
  6. [6] Glebov N.I., On a generalization of the Kakutani fixed point theorem, Soviet Math. Dokl., 1969, 10(2), 446–448 Zbl0187.07503
  7. [7] Glicksberg I.L., A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc., 1952, 3(1), 170–174 Zbl0046.12103
  8. [8] Morgan J., Raucci R., Lower semicontinuity for approximate social Nash equilibria, Internat. J. Game Theory, 2002, 31(4), 499–509 http://dx.doi.org/10.1007/s001820300134 Zbl1072.91001
  9. [9] Nash J.F. Jr., Equilibrium points in n-person games, Proc. Nat. Acad. Sci. U.S.A., 1950, 36, 48–49 http://dx.doi.org/10.1073/pnas.36.1.48 Zbl0036.01104
  10. [10] Puu T., On the stability of Cournot equilibrium when the number of competitors increases, J. Econom. Behavior Organization, 2008, 66(3–4), 445–456 http://dx.doi.org/10.1016/j.jebo.2006.06.010 

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