Common fixed points of mappings satisfying implicit relations in partial metric spaces
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Authors
Calogero Vetro
- Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, via Archirafi 34, 90123 Palermo, Italy.
Francesca Vetro
- DEIM, Universita degli Studi di Palermo, Viale delle Scienze, 90128 Palermo, Italy.
Abstract
Matthews, [S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology
and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], introduced and studied
the concept of partial metric space, as a part of the study of denotational semantics of data
flow networks.
He also obtained a Banach type fixed point theorem on complete partial metric spaces. Very recently
Berinde and Vetro, [V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive
conditions, Fixed Point Theory and Applications 2012, 2012:105], discussed, in the setting of metric and
ordered metric spaces, coincidence point and common fixed point theorems for self-mappings in a general
class of contractions defined by an implicit relation. In this work, in the setting of partial metric spaces,
we study coincidence point and common fixed point theorems for two self-mappings satisfying generalized
contractive conditions, defined by implicit relations. Our results unify, extend and generalize some related
common fixed point theorems of the literature.
Share and Cite
ISRP Style
Calogero Vetro, Francesca Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 3, 152--161
AMA Style
Vetro Calogero, Vetro Francesca, Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl. (2013); 6(3):152--161
Chicago/Turabian Style
Vetro, Calogero, Vetro, Francesca. "Common fixed points of mappings satisfying implicit relations in partial metric spaces." Journal of Nonlinear Sciences and Applications, 6, no. 3 (2013): 152--161
Keywords
- Coincidence point
- common fixed point
- contraction
- implicit relation
- partial metric space.
MSC
References
-
[1]
M. Abbas, D. Ilic, Common fixed points of generalized almost nonexpansive mappings, Filomat , 24:3 (2010), 11-18.
-
[2]
J. Ali, M. Imdad, Unifying a multitude of common fixed point theorems employing an implicit relation, Commun. Korean Math. Soc., 24 (2009), 41-55.
-
[3]
A. Aliouche, A. Djoudi, Common fixed point theorems for mappings satisfying an implicit relation without decreasing assumption, Hacet. J. Math. Stat. , 36 (2007), 11-18.
-
[4]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces , Topology Appl. , 159 (2012), 3234-3242.
-
[5]
H. Aydi, C. Vetro, W. Sintunavarat, P. Kumam, Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory Appl. , 2012 (2012), 124
-
[6]
G. V. R. Babu, M. L. Sandhy, M. V. R. Kameshwari, A note on a fixed point theorem of Berinde on weak contractions, Carpathian J. Math. , 24 (2008), 8-12.
-
[7]
S. Banach , Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. , 3 (1922), 133-181.
-
[8]
V. Berinde, Stability of Picard iteration for contractive mappings satisfying an implicit relation , Carpathian J. Math. , 27 (2011), 13-23.
-
[9]
V. Berinde, Approximating fixed points of implicit almost contractions, Hacet. J. Math. Stat. , 40 (2012), 93-102.
-
[10]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012 (2012), 105
-
[11]
S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. , 25 (1972), 727-730.
-
[12]
M. Cherichi, B. Samet, Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations, Fixed Point Theory Appl. , 2012 (2012), 13
-
[13]
L. Ćirić, R. P. Agarwal, B. Samet , Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory Appl. , 2011 (2011), 56
-
[14]
C. Di Bari, P. Vetro, Common fixed points for \(\psi\)-contractions on partial metric spaces, to appear in Hacettepe Journal of Mathematics and Statistics, (),
-
[15]
C. Di Bari, P. Vetro, Fixed points for weak \(\varphi\)-contractions on partial metric spaces, Int. J. of Engineering, Contemporary Mathematics and Sciences , 1 (2011), 5-13.
-
[16]
Z. Golubović, Z. Kadelburg, S. Radenović, Common fixed points of ordered g-quasicontractions and weak contractions in ordered metric spaces, Fixed Point Theory Appl., 2012 (2012), 20
-
[17]
G. E. Hardy, T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. , 16 (1973), 201-206.
-
[18]
M. Jleli, V. Ćojbašić Rajić, B. Samet, C. Vetro , Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations, J. Fixed Point Theory Appl. , doi:10.1007/s11784-012-0081-4. (2012)
-
[19]
R. Kannan , Some results on fixed points, Bull. Calcutta Math. Soc. , 10 (1968), 71-76.
-
[20]
S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci. , 728 (1994), 183-197.
-
[21]
H. K. Nashine, B. Samet, C. Vetro , Fixed point theorems in partially ordered metric spaces and existence results for integral equations, Numer. Funct. Anal. Optim. , 33 (2012), 1304-1320.
-
[22]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239.
-
[23]
S. Oltra, O. Valero , Banach's fixed point theorem for partial metric spaces , Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26.
-
[24]
S. J. O'Neill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., 806 (1996), 304-315.
-
[25]
D. Paesano, P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920.
-
[26]
V. Popa , Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacău, 7 (1997), 127-133.
-
[27]
V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math., 32 (1999), 157-163.
-
[28]
V. Popa, M. Imdad, J. Ali, Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces, Bull. Malays. Math. Sci. Soc. , 33 (2010), 105-120.
-
[29]
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.
-
[30]
S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., Article ID 493298, (2010), 6 pages.
-
[31]
S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Math. Struct. in Comp. Science, 19 (2009), 541-563.
-
[32]
I. A. Rus, A. Petruşel, G. Petruşel , Fixed Point Theory , Cluj University Press, Cluj-Napoca (2008)
-
[33]
M. P. Schellekens, The correspondence between partial metrics and semivaluations , Theoret. Comput. Sci. , 315 (2004), 135-149.
-
[34]
M. Turinici , Abstract comparison principles and multivariable Gronwall-Bellman inequalities, J. Math. Anal. Appl. , 117 (1986), 100-127.
-
[35]
O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6 (2005), 229-240.
-
[36]
C. Vetro, Common fixed points in ordered Banach spaces, Le Matematiche , 63 (2008), 93-100.
-
[37]
F. Vetro, S. Radenović, Nonlinear \(\psi\)-quasi-contractions of Ćirić-type in partial metric spaces, Appl. Math. Comput. , 219 (2012), 1594-1600.
-
[38]
P. Waszkiewicz, Partial metrisability of continuous posets, Math. Struct. in Comp. Science, 16 (2006), 359-372.