A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces
-
1661
Downloads
-
2641
Views
Authors
Valeriu Popa
- Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences ''Vasile Alecsandri'' University of Bacău, 157 Calea Mărăşeşti, Bacău, 600115, Romania.
Alina-Mihaela Patriciu
- Department of Mathematics, Informatics and Educational Sciences, Faculty of Sciences ''Vasile Alecsandri'' University of Bacău, 157 Calea Mărăşeşti, Bacău, 600115, Romania.
Abstract
In this paper a general fixed point theorem in G-metric spaces for weakly compatible mappings is proved,
theorem which generalize the results from Abbas et. al. [M. Abbas and B. E. Rhoades, Appl. Math.
and Computation 215 (2009), 262 - 269] and [M. Abbas, T. Nazir and S. Radanović, Appl. Math. and
Computation 217 (2010), 4094 - 4099]. In the last part of this paper it is proved that the fixed point problem
for these mappings is well posed.
Share and Cite
ISRP Style
Valeriu Popa, Alina-Mihaela Patriciu, A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 2, 151--160
AMA Style
Popa Valeriu, Patriciu Alina-Mihaela, A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces. J. Nonlinear Sci. Appl. (2012); 5(2):151--160
Chicago/Turabian Style
Popa, Valeriu, Patriciu, Alina-Mihaela. "A general fixed point theorem for pairs of weakly compatible mappings in G--metric spaces." Journal of Nonlinear Sciences and Applications, 5, no. 2 (2012): 151--160
Keywords
- G-metric space
- weakly compatible mappings
- fixed point.
MSC
References
-
[1]
M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. and Computation, 215 (2009), 262 - 269.
-
[2]
M. Abbas, T. Nazir, S. Radanović, Some periodic point results in generalized metric spaces, Appl. Math. and Computation, 217 (2010), 4094 - 4099.
-
[3]
M. Akkouchi, V. Popa, Well posedness of common fixed point problem for three mappings under strict contractive conditions, Bull. Math. Inform. Physics, Petroleum - Gas Univ. Ploiesti , 61 (2009), 1 - 10.
-
[4]
M. Akkouchi, V. Popa, Well posedness of a fixed point problem using G - function, Sc. St. Res. Univ. Vasile Alecsandri, Bacau. Ser. Math. Inform., 20 (2010), 5 - 12.
-
[5]
M. Akkouchi, V. Popa, Well posedness of fixed point problem for mappings satisfying an implicit relation, Demonstratio Math. , 43, 4 (2010), 923 - 929.
-
[6]
R. Chung, T. Kadian, A. Rosie, B. E. Rhoades, Property (P) in G - metric spaces , Fixed Point Theory and Applications, Article ID 401684, 2010 (2010), 12 pages.
-
[7]
L. B. Ciric , A generalization of Banach contractions, Proc. Amer. Math. , 45 (1974), 267 - 273.
-
[8]
F. S. De Blassi et J. Myjak, Sur la porosite de contractions sans point fixe, Comptes Rend. Acad. Sci. Paris , 308 (1989), 51 - 54.
-
[9]
B. C. Dhage, Generalized metric spaces and mappings with fixed point, , Bull. Calcutta Math. Soc. , 84 (1992), 329 - 336.
-
[10]
B. C. Dhage, Generalized metric spaces and topological structures I, Anal. St. Univ. Al. I. Cuza, Iasi Ser. Mat., 46, 1 (2000), 3 - 24.
-
[11]
G. Jungck, Common fixed points for noncontinuous, nonself maps on nonnumeric spaces, Far East J. Math. Sci., 4(2) (1996), 195-215.
-
[12]
B. K. Lahiri, P. Das , Well posedness and porosity of certain classes of operators, Demonstratio Math. , 38 (2005), 170 - 176.
-
[13]
S. Manro, S. S. Bahtia, S. Kumar, Expansion mappings theorems in G - metric spaces, Intern. J. Contemp. Math. Sci. , 5 (2010), 2529 - 2535.
-
[14]
Z. Mustafa, B. Sims , Some remarks concerning D - metric spaces, Intern. Conf. Fixed Point. Theory and Applications, Yokohama, (2004), 189 - 198.
-
[15]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Analysis , 7 (2006), 289 - 297.
-
[16]
Z. Mustafa, H. Obiedat, F. Awadeh, Some fixed point theorems for mappings on G - complete metric spaces, Fixed Point Theory and Applications, Article ID 189870, 2008 (2008), 12 pages.
-
[17]
Z. Mustafa, W. Shatanawi, M. Bataineh, Fixed point theorem on uncomplete G - metric spaces, J. Math. Statistics, 4(4) (2008), 196 - 201.
-
[18]
Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G - metric spaces, Fixed Point Theory and Applications, Article ID 917175, 2009 (2009), 10 pages.
-
[19]
Z. Mustafa, W. S. Shatanawi, M. Bataineh, Existence of fixed point results in G - metric spaces, Intern. J. Math. Math. Sci., Article ID 283028, 2009 (2009), 10 pages.
-
[20]
Z. Mustafa and H. Obiedat , A fixed point theorem of Reich in G - metric spaces, Cuba A. Math. J., 12 (2010), 83 - 93.
-
[21]
H. Obiedat, Z. Mustafa, Fixed results on a nonsymmetric G - metric spaces, Jordan. J. Math. Statistics, 3(2) (2010), 65 - 79.
-
[22]
R. P. Pant, Common fixed point for noncommuting mappings , J. Math. And Appl., 188 (1994), 436 - 440.
-
[23]
R. P. Pant, Common fixed point for four mappings, Bull. Calcutta Math. Soc., 9 (1998), 281 - 286.
-
[24]
A. Petrusel, I. A. Rus, J. C. Yao, Well-posedness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese J.Math., 11, 3 (2007), 903 - 912.
-
[25]
V. Popa , Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat., Univ. Bacau , 7 (1997), 129 - 133.
-
[26]
V. Popa, Some fixed point theorems for compatible mappings satisfying implicit relations, Demonstratio Math., 32, 1 (1999), 157 - 163.
-
[27]
V. Popa, Well posedness of fixed problem in orbitally complete metric spaces, Stud. Cerc. St. Ser. Math. Univ. Bacau, Suppl., 16 (2006), 209 - 214.
-
[28]
V. Popa, Well posedness of fixed point problem in compact metric spaces, Bull. Math. Inform. Physics Series, Petroleum - Gas Univ. Ploiesti , 60, 1 (2008), 1 - 4.
-
[29]
S. Reich, A. J. Zaslavski , Well posedness of fixed point problems, Far East J. Math. Sci. Special volume, Part. III, (2001), 393 - 401.
-
[30]
I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca (2008)
-
[31]
I. A. Rus, Picard operators and well-posedness of fixed point problems, Studia Univ. Babes - Bolyai, Mathematica , 52, 3 (2007), 147 - 156.
-
[32]
I. A. Rus, A. Petrusel, G. Petrusel, Fixed Point Theory, Cluj University Press, Cluj Napoca (2008)
-
[33]
W. Shatanawi , Fixed point theory for contractive mappings satisfying \(\Phi\) - maps in G - metric spaces, Fixed Point Theory and Applications, Article ID 181650, 2010 (2010), 9 pages.