Two general fixed point theorems for a sequence of mappings satisfying implicit relations in Gp - metric spaces

Valeriu Popa, Alina-Mihaela Patriciu

Abstract

In this paper, two general fixed point theorem for a sequence of mappings satisfying implicit relations in Gp - complete metric spaces are proved.


Keywords

Gp - complete metric space; sequence of mappings; fixed point; implicit relation.

Subject classification

47H10; 54H25.

Full Text:

PDF

References

M. Abbas, T. Nazir and S. Radenovic, Some periodic point results in generalized metric spaces, Appl. Math. Comput. 217 (2010), 4084-4099.

http://dx.doi.org/10.1016/j.amc.2010.10.026

T. Abdeljawad, E. Karapinar and K. Tas, Existence and uniqueness of common fixed points on partial metric spaces, Applied Math. Lett. 24 (11) (2011), 1894-1899.

http://dx.doi.org/10.1016/j.aml.2011.05.014

I. Altun, F. Sola and H. Simsek, Generalized contractive principle on partial metric spaces, Topology Appl. 157 (18) (2010), 2778-2785.

http://dx.doi.org/10.1016/j.topol.2010.08.017

H. Aydi, E. Karapinar and P. Salimi, Some fixed point results in Gp - metric spaces, J. Appl. Math. (2012), Article ID 891713.

http://dx.doi.org/10.1155/2012/891713

M. A. Barakat and A. M. Zidan, A common fixed point theorem for weak contractive maps in Gp - metric spaces, J. Egyptean Math. Soc. (2014), DOI: 10.1016/j.joems.2014.06.008.

http://dx.doi.org/10.1016/j.joems.2014.06.008

N. Bilgili, E. Karapinar and P. Salimi, Fixed point theorems for generalized contractions on Gp - metric spaces, J. Ineq. Appl. (2013), 2013:39.

http://dx.doi.org/10.1186/1029-242X-2013-39

R. Chi, E. Karapinar and T. D. Than, A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (5 - 6) (2012), 1673-1681.

B. C. Dhage, Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 8 (1992), 329-336.

B. C. Dhage, Generalized metric spaces and topological structures, I, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. 46 (2000), 3-24.

Z. Kadelburg, H. K. Nashine and S. Radanovic, Fixed point results under various contractive conditions in partial metric spaces, RACSAM 10 (2013), 241-256.

http://dx.doi.org/10.1007/s13398-012-0066-6

E. Karapinar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett. 24 (11) (2011), 1894-1899.

http://dx.doi.org/10.1016/j.aml.2011.05.013

D. S. Kaushal and S. S. Pagey, Some results of fixed point theorems on complete G - metric spaces, South Asian J. Math. 2 (4) (2014), 318-324.

S. Matthews, Partial metric topology and applications, Proc. 8th Summer Conf. General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183-197.

http://dx.doi.org/10.1111/j.1749-6632.1994.tb44144.x

G. Meena and D. Nema, Common fixed point theorem for a sequence of mappings in G - metric spaces, Intern. J. Math. Computer Research 2, 5 (2014), 403-407.

S. K. Mohanta, Some fixed point theorems in G - metric spaces, An. Stiint. Univ. Ovidius, Constanta. Ser. Mat. 20 (1) (2012), 285-306.

Z. Mustafa and B. Sims, Some remarks concerning D - metric spaces, Proc. Conf. Fixed Point Theory Appl., Valencia (Spain) (2003), 189-198.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.

Z. Mustafa, H. Obiedat, and F. Awawdeh, Some fixed point theorem for mapping on complete G - metric spaces, Fixed Point Theory Appl. (2008), Article ID 189870.

Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G - metric spaces, Fixed Point Theory Appl. (2009), Article ID 917175.

Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G - metric spaces, Intern. J. Math. Math. Sci. (2009), Article ID 283028.

Z. Mustafa and H. Obiedat, A fixed point theorem of Reich in G - metric spaces, Cubo. A Math. J. 12 (1) (2010), 83-93.

Z. Mustafa, M. Khandagji and W. Shatanawi, Fixed point results on complete G - metric spaces, St. Sci. Math. Hungarica 48 (3) (2011), 304-319.

V. Popa, Fixed point theorems for implicit contractive mappings, St. Cerc. Stiint.. Ser. Mat. 7 (1997), 129-133.

V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math. 32 (1) (1999), 157-163.

V. Popa, A general fixed point theorem for several mappings in G - metric spaces, Sci. Stud. Res. Ser. Math. Inform. 21 (1) (2011), 205-214.

V. Popa and A.-M. Patriciu, Two general fixed point theorems for pairs of weakly compatible mappings in G - metric spaces, Novi Sad J. Math. 42, 2 (2013), 49-60.

V. Popa and A.-M. Patriciu, A general fixed point theorem for mappings satisfying an phi - implicit relation in complete G - metric spaces, Gazi Univ. J. Sci. 25 (2) (2012), 403-408.

V. Popa and A.-M. Patriciu, A general fixed point theorem for pair of weakly compatible mappings in G - metric spaces, J. Nonlinear Sci. Appl. 5 (2) (2012), 151-160.

V. Popa and A.-M. Patriciu, Fixed point theorems for mappings satisfying an implicit relation in complete G - metric spaces, Bul. Instit. Politehn. Iasi 50 (63), Ser. Mat. Mec. Teor. Fiz., 2 (2013), 97-123.

W. Shatanawi, Fixed point theory for contractive mappings satisfying - maps in G - metric spaces, Fixed Point Theory Appl. (2010), Article ID 181650.

W. Shatanawi, Common fixed point results for self - maps in G - metric spaces, Mat. Vesnik. 65 (2) (2013), 143-150.

W. Shatanawi and M. Postolache, Some fixed point results for a G - weak contraction in G - metric spaces, Abstr. Appl. Anal. (2012), Article ID 815870.

W. Shatanawi, S. Chauhan, M. Postolache, N. Abbas amd S. Radenovic, Common fixed point for contractive mappings in G - metric spaces, J. Adv. Math. Stud. 6 (1) (2013), 53-72.

R. Srivastava, S. Agrawal, R. Bhardwaj and R. Vardava, Fixed point theorems in complete G - metric spaces, South Asian J. Math. 2 (2) (2013), 167-174.

R. K. Vats, S. Kumar and V. Sihang, Fixed point theorems in complete G - metric spaces, Fasc. Math. 47 (2011), 127-139.

C. Vetro and F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. 6 (2013), 152-161.

M. R. A. Zand and A. N. Nezhad, A generalization of partial metric spaces, J. Contemporary Appl. Math. 1 (1) (2011), 86-93.

Abstract Views

1966
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt