Geodesic
Rectangular b-metric space and contraction principles :
George, R. 1   ; Radenović, S. 2   ; Reshma, K. P. 3   ; Shukla, S. 4
1 Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarh, India
2 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia
3 Department of Mathematics, Government VYT PG Autonomous College, Durg, Chhattisgarh, India
4 Department of Applied Mathematics, S.V.I.T.S. Indore (M.P.), India
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 1005-1013 Cet article a éte moissonné depuis la source International Scientific Research Publications

Voir la notice de l'article

The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular metric space and b-metric space. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

DOI : 10.22436/jnsa.008.06.11
Classification : 47H10
Keywords: Fixed points, b-metric space, rectangular metric space, rectangular b-metric space.

George, R.  1   ; Radenović, S.  2   ; Reshma, K. P.  3   ; Shukla, S.  4

1 Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarh, India
2 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia
3 Department of Mathematics, Government VYT PG Autonomous College, Durg, Chhattisgarh, India
4 Department of Applied Mathematics, S.V.I.T.S. Indore (M.P.), India 
@article{10_22436_jnsa_008_06_11,
     author = {George, R. and Radenovi\'c, S. and Reshma, K. P. and Shukla, S.},
     title = {Rectangular b-metric space and contraction principles},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {1005-1013},
     year = {2015},
     volume = {8},
     number = {6},
     doi = {10.22436/jnsa.008.06.11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.11/}
}
TY  - JOUR
AU  - George, R.
AU  - Radenović, S.
AU  - Reshma, K. P.
AU  - Shukla, S.
TI  - Rectangular b-metric space and contraction principles
JO  - Journal of nonlinear sciences and its applications
PY  - 2015
SP  - 1005
EP  - 1013
VL  - 8
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.11/
DO  - 10.22436/jnsa.008.06.11
LA  - en
ID  - 10_22436_jnsa_008_06_11
ER  - 
%0 Journal Article
%A George, R.
%A Radenović, S.
%A Reshma, K. P.
%A Shukla, S.
%T Rectangular b-metric space and contraction principles
%J Journal of nonlinear sciences and its applications
%D 2015
%P 1005-1013
%V 8
%N 6
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.06.11/
%R 10.22436/jnsa.008.06.11
%G en
%F 10_22436_jnsa_008_06_11
George, R.; Radenović, S.; Reshma, K. P.; Shukla, S. Rectangular b-metric space and contraction principles. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 1005-1013. doi: 10.22436/jnsa.008.06.11

[1] Abdeljawad, T.; Turkoglu, D. Locally convex valued rectangular metric spaces and Kannan's fixed point theorem, arXiv, Volume 2011 (2011), pp. 1-11

[2] Aydi, H.; Bota, M. F.; Karapinar, E.; Moradi, S. A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, Volume 13 (2012), pp. 337-346

[3] Azam, A.; Arshad, M. Kannan Fixed Point Theorems on generalised metric spaces , J. Nonlinear Sci. Appl., Volume 2008 (1), pp. 45-48

[4] Azam, A.; Arshad, M.; Beg, I. Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math., Volume 3 (2009), pp. 236-241

[5] I. A. Bakhtin The contraction mapping principle in quasimetric spaces , Funct. Anal., Unianowsk Gos. Ped. Inst., Volume 30 (1989), pp. 26-37

[6] Boriceanu, M. Strict fixed point theorems for multivalued operators in b-metric spaces , Inter. J. Mod. Math., Volume 4 (2009), pp. 285-301

[7] Boriceanu, M.; Bota, M.; Petrusel, A. Mutivalued fractals in b-metric spaces, Cen. Eur. J. Math., Volume 8 (2010), pp. 367-377

[8] Bota, M.; Molnar, A.; Csaba, V. On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, Volume 12 (2011), pp. 21-28

[9] Branciari, A. A fixed point theorem of Banach-Caccippoli type on a class of generalised metric spaces, Publ. Math. Debrecen, Volume 57 (2000), pp. 31-37

[10] Chen, C. N. Common fixed point theorem in complete generalized metric spaces, J. Appl. Math., Volume 2012 (2012), pp. 1-14

[11] S. Czerwik Contraction mappings in b-metric spaces , Acta. Math. Inform. Univ. Ostraviensis, Volume 1 (1993), pp. 5-11

[12] S. Czerwik Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, Volume 46 (1998), pp. 263-276

[13] Czerwik, S.; Dlutek, K.; S. L. Singh Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci. , Volume 11 (1997), pp. 87-94

[14] Czerwik, S.; Dlutek, K.; S. L. Singh Round-off stability of iteration procedures for set valued operators in b-metric spaces, J. Natur. Phys. Sci., Volume 15 (2001), pp. 1-8

[15] Das, P. A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sci., Volume 9 (2002), pp. 29-33

[16] Das, P. A fixed point theorem in generalized metric spaces , Soochow J. Math., Volume 33 (2007), pp. 33-39

[17] Das, P.; B. K. Lahri Fixed point of a Ljubomir Ciric's quasi-contraction mapping in a generalized metric space , Publ. Math. Debrecen, Volume 61 (2002), pp. 589-594

[18] Das, P.; B. K. Lahri Fixed Point of contractive mappings in generalised metric space, Math. Slovaca, Volume 59 (2009), pp. 499-504

[19] Erhan, I. M.; Karapinar, E.; Sekulic, T. Fixed Points of (psi, phi) contractions on generalised metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-12

[20] George, R.; Fisher, B. Some generalised results of fixed points in cone b-metric spaces , Math. Moravic., Volume 17 (2013), pp. 39-50

[21] Jeong, G. S.; Rhoades, B. E. Maps for which\( F(T) = F(T^n)\), Fixed Point Theory Appl., Volume 6 (2007), pp. 71-105

[22] Jleli, M.; Samet, B. The Kannan's fixed point theorem in cone rectangular metric space, J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 161-167

[23] Lakzian, H.; Samet, B. Fixed Points for (\(\psi,\phi\))-weakly contractive mapping in generalised metric spaces, Appl. Math. Lett., Volume 25 (2012), pp. 902-906

[24] S. G. Mathews Partial Metric Topology, Papers on general topology appl., Ann. New York Acad. Sci., Volume 728 (1994), pp. 183-197

[25] Mihet, D. On Kannan fixed point result in generalised metric spaces, J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 92-96

[26] Sarma, I. R.; Rao, J. M.; Rao, S. S. Contractions over generalised metric spaces, J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 180-182

Cité par Sources :