Fixed point results for multivalued contractions on ordered gauge spaces

Gabriela Petruşel

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 520-528
  • ISSN: 2391-5455

Abstract

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The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].

How to cite

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Gabriela Petruşel. "Fixed point results for multivalued contractions on ordered gauge spaces." Open Mathematics 7.3 (2009): 520-528. <http://eudml.org/doc/269251>.

@article{GabrielaPetruşel2009,
abstract = {The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].},
author = {Gabriela Petruşel},
journal = {Open Mathematics},
keywords = {Gauge space; Multivalued operator; Fixed point; Data dependence; gauge space; multivalued operator; fixed point; data dependence},
language = {eng},
number = {3},
pages = {520-528},
title = {Fixed point results for multivalued contractions on ordered gauge spaces},
url = {http://eudml.org/doc/269251},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Gabriela Petruşel
TI - Fixed point results for multivalued contractions on ordered gauge spaces
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 520
EP - 528
AB - The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].
LA - eng
KW - Gauge space; Multivalued operator; Fixed point; Data dependence; gauge space; multivalued operator; fixed point; data dependence
UR - http://eudml.org/doc/269251
ER -

References

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  1. [1] Agarwal R.P., Dshalalow J., O’Regan D., Fixed point and homotopy results for generalized contractive maps of Reich-type, Appl. Anal., 2003, 82, 329–350 http://dx.doi.org/10.1080/0003681031000098470 Zbl1039.47030
  2. [2] Chiş A., Precup R., Continuation theory for general contractions in gauge spaces, Fixed Point Theory Appl., 2004, 3, 173–185 Zbl1087.47050
  3. [3] Ćirić L.B., Fixed points for generalized multi-valued contractions, Mat. Vesnik, 1972, 9, 265–272 Zbl0258.54043
  4. [4] Ćirić L., Cakic N., Rajovic M., Ume J.S., Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2008, ID 131294, 11 pages Zbl1158.54019
  5. [5] Dugundji J., Topology, Allyn & Bacon, Boston, 1966 
  6. [6] Espínola R., Petruşel A., Existence and data dependence of fixed points for multivalued operators on gauge spaces, J. Math. Anal. Appl., 2005, 309, 420–432 http://dx.doi.org/10.1016/j.jmaa.2004.07.006 Zbl1070.47046
  7. [7] Frigon M., Fixed point results for multivalued contractions in gauge spaces and applications, Set Valued Mappings with Applications in Nonlinear Analysis, Ser. Math. Anal. Appl., Vol. 4, Taylor & Francis, London, 2002, 175–181 
  8. [8] Frigon M., Fixed point and continuation results for contractions in metric and gauge spaces, Banach Center Publ., 2007, 77, 89–114 http://dx.doi.org/10.4064/bc77-0-8 Zbl1122.47045
  9. [9] Lakshmikantham V., Ciric L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, T.M.A., 2009, 70, 4341–4349 http://dx.doi.org/10.1016/j.na.2008.09.020 Zbl1176.54032
  10. [10] Petruşel A., Petruşel G., Multivalued contractions of Feng-Liu type in complete gauge spaces, preprint Zbl1249.54088
  11. [11] Petruşel G., Existence and data dependence of fixed points and strict fixed points for mulivalued Y-contractions, Carpathian J. Math., 2007, 23, 172–176 Zbl1164.54388
  12. [12] Reich S., Fixed point of contractive functions, Boll. Un. Mat. Ital., 1972, 5, 26–42 Zbl0249.54026
  13. [13] Rus I.A., Generalized Contractions and Applications, Transilvania Press Cluj-Napoca, 2001 
  14. [14] Rus I.A., Fixed point theorems for multivalued mappings in complete metric spaces, Mathematica Japonica, 1975, 20, 21–24 Zbl0336.54047
  15. [15] Rus I.A., Petruşel A., Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 2005, 134, 411–419 http://dx.doi.org/10.1090/S0002-9939-05-07982-7 Zbl1086.47026
  16. [16] Rus I.A., Petruşel A., Petruşel G., Fixed point theorems for set-valued Y -contractions, Banach Center Publications, Fixed Point Theory and its Applications, 2007, 77, 227–237 http://dx.doi.org/10.4064/bc77-0-17 Zbl1126.47047

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