Fixed points for non-self operators in gauge spaces
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Authors
Tania Lazăr
- Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului Street no. 28, 400114, Cluj-Napoca, Romania.
Gabriela Petruşel
- Department of Business, Babeş-Bolyai University, Horia Street no. 7, 400174 Cluj-Napoca, Romania.
Abstract
The purpose of this article is to present some local fixed point results for generalized contractions on (ordered)
complete gauge space. As a consequence, a continuation theorem is also given. Our theorems generalize
and extend some recent results in the literature.
Share and Cite
ISRP Style
Tania Lazăr, Gabriela Petruşel, Fixed points for non-self operators in gauge spaces, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 1, 29--34
AMA Style
Lazăr Tania, Petruşel Gabriela, Fixed points for non-self operators in gauge spaces. J. Nonlinear Sci. Appl. (2013); 6(1):29--34
Chicago/Turabian Style
Lazăr, Tania, Petruşel, Gabriela. "Fixed points for non-self operators in gauge spaces." Journal of Nonlinear Sciences and Applications, 6, no. 1 (2013): 29--34
Keywords
- gauge space
- generalized contraction
- fixed point
- ordered gauge space
- continuation theorem.
MSC
References
-
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Anal., 87 (2008), 109-116.
-
[2]
A. Amini-Harandi, H. Emami , A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. TMA, 72 (2010), 2238-2242.
-
[3]
J. Caballero, J. Harjani, K. Sadarangani, Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations, Fixed Point Theory Appl., Article ID 916064, 2010 (2010), 14 pages.
-
[4]
C. Chifu, G. Petruşel, Fixed-point results for generalized contractions on ordered gauge spaces with applications, Fixed Point Theory Appl., Article ID 979586, 2011 (2011), 10 pages.
-
[5]
J. Dugundji, Topology, Allyn & Bacon, Boston (1966)
-
[6]
M. Fréchet , Les espaces abstraits, Gauthier-Villars, Paris (1928)
-
[7]
M. Frigon, Fixed point and continuation results for contractions in metric and gauge spaces, Banach Center Publ., 77 (2007), 89-114.
-
[8]
J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. Theory, Methods & Applications, 71 (2009), 3403-3410.
-
[9]
J. Harjani, K. Sadarangani, Fixed point theorems for monotone generalized contractions in partially ordered metric spaces and applications to integral equations, J. Convex Analysis, 19 (2012), 853-864.
-
[10]
J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces , Nonlinear Anal. TMA, 74 (2011), 768-774.
-
[11]
H. K. Nashine, B. Samet, C. Vetro , Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Computer Modelling, 54 (2011), 712-720.
-
[12]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239.
-
[13]
J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135 (2007), 2505-2517.
-
[14]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations , Acta Math. Sinica-English Series, 23 (2007), 2205-2212.
-
[15]
D. O'Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. , 341 (2008), 1241-1252.
-
[16]
A. Petruşel, I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. , 134 (2006), 411-418.
-
[17]
G. Petruşel, Fixed point results for multivalued contractions on ordered gauge spaces, Central Eurropean J. Math. , 7 (2009), 520-528.
-
[18]
G. Petruşel, I. Luca, Strict fixed point results for multivalued contractions on gauge spaces, Fixed Point Theory, 11 (2010), 119-124.
-
[19]
A. C. M. Ran, M. C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , 132 (2004), 1435-1443.
-
[20]
I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory , 9 (2008), 541-559.
-
[21]
I. A. Rus, A. Petruşel, G. Petruşel, Fixed Point Theory, Cluj University Press, Cluj-Napoca (2008)
-
[22]
R. Saadati, S. M. Vaezpour, Monotone generalized weak contractions in partially ordered metric spaces , Fixed Point Theory, 11 (2010), 375-382.