Fixed point results for multivalued contractions on ordered gauge spaces
Gabriela Petruşel
Open Mathematics, Tome 7 (2009), p. 520-528 / Harvested from The Polish Digital Mathematics Library

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].

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:269251
@article{bwmeta1.element.doi-10_2478_s11533-009-0027-2,
     author = {Gabriela Petru\c sel},
     title = {Fixed point results for multivalued contractions on ordered gauge spaces},
     journal = {Open Mathematics},
     volume = {7},
     year = {2009},
     pages = {520-528},
     zbl = {1203.54044},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0027-2}
}
Gabriela Petruşel. Fixed point results for multivalued contractions on ordered gauge spaces. Open Mathematics, Tome 7 (2009) pp. 520-528. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0027-2/

[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 | Zbl 1039.47030

[2] Chiş A., Precup R., Continuation theory for general contractions in gauge spaces, Fixed Point Theory Appl., 2004, 3, 173–185 | Zbl 1087.47050

[3] Ćirić L.B., Fixed points for generalized multi-valued contractions, Mat. Vesnik, 1972, 9, 265–272 | Zbl 0258.54043

[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 | Zbl 1158.54019

[5] Dugundji J., Topology, Allyn & Bacon, Boston, 1966

[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 | Zbl 1070.47046

[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] 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 | Zbl 1122.47045

[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 | Zbl 1176.54032

[10] Petruşel A., Petruşel G., Multivalued contractions of Feng-Liu type in complete gauge spaces, preprint | Zbl 1249.54088

[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 | Zbl 1164.54388

[12] Reich S., Fixed point of contractive functions, Boll. Un. Mat. Ital., 1972, 5, 26–42 | Zbl 0249.54026

[13] Rus I.A., Generalized Contractions and Applications, Transilvania Press Cluj-Napoca, 2001

[14] Rus I.A., Fixed point theorems for multivalued mappings in complete metric spaces, Mathematica Japonica, 1975, 20, 21–24 | Zbl 0336.54047

[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 | Zbl 1086.47026

[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 | Zbl 1126.47047