Geodesic
On some common coupled fixed point results in rectangular $b$-metric spaces
Gu, Feng1
1 Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4085-4098.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, by using the $w$-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular $b$-metrics. Some new common coupled fixed point theorems are obtained. We also provide illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.
DOI : 10.22436/jnsa.010.08.05
Classification : 47H10, 54H25
Keywords: Rectangular b-metric space, coupled coincidence point, common coupled fixed point, w-compatible mapping pairs.

Gu, Feng 1

1 Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China 
@article{JNSA_2017_10_8_a4,
     author = {Gu, Feng},
     title = {On some common coupled fixed point results in rectangular \(b\)-metric spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {4085-4098},
     publisher = {mathdoc},
     volume = {10},
     number = {8},
     year = {2017},
     doi = {10.22436/jnsa.010.08.05},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.05/}
}
TY  - JOUR
AU  - Gu, Feng
TI  - On some common coupled fixed point results in rectangular \(b\)-metric spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 4085
EP  - 4098
VL  - 10
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.05/
DO  - 10.22436/jnsa.010.08.05
LA  - en
ID  - JNSA_2017_10_8_a4
ER  - 
%0 Journal Article
%A Gu, Feng
%T On some common coupled fixed point results in rectangular \(b\)-metric spaces
%J Journal of nonlinear sciences and its applications
%D 2017
%P 4085-4098
%V 10
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.05/
%R 10.22436/jnsa.010.08.05
%G en
%F JNSA_2017_10_8_a4
Gu, Feng. On some common coupled fixed point results in rectangular \(b\)-metric spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4085-4098. doi : 10.22436/jnsa.010.08.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.05/

[1] Abbas, M.; Khan, M. A.; Radenović, S. Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., Volume 217 (2010), pp. 195-202 | DOI

[2] Abdeljawad, T.; D. Türkoğlu Locally convex valued rectangular metric spaces and the Kannan’s fixed point theorem, J. Comput. Anal. Appl., Volume 14 (2012), pp. 484-494 | Zbl

[3] Arshad, M.; Ahmad, J.; E. Karapınar Some common fixed point results in rectangular metric spaces, Int. J. Anal., Volume 2013 (2013), pp. 1-7

[4] Aydi, H.; Felhi, A.; Sahmim, S. Common fixed points in rectangular b-metric spaces using (E.A) property, J. Adv. Math. Stud., Volume 8 (2015), pp. 159-169 | Zbl

[5] Aydi, H.; Karapınar, E.; Lakzian, H. Fixed point results on a class of generalized metric spaces, Math. Sci. (Springer), Volume 2012 (2012), pp. 1-6 | DOI

[6] Branciari, A. A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, Volume 57 (2000), pp. 31-37 | Zbl

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

[8] Bari, C. Di; P. Vetro Common fixed points in generalized metric spaces , Appl. Math. Comput., Volume 218 (2012), pp. 7322-7325

[9] Ding, H.-S.; Imdad, M.; Radenović, S.; J. Vujaković On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab J. Math. Sci., Volume 22 (2016), pp. 151-164 | Zbl | DOI

[10] Erhan, ˙I. M.; Karapınar, E.; Sekulić, T. Fixed points of (\(\psi,\phi\)) contractions on rectangular metric spaces , Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-12 | Zbl | DOI

[11] George, R.; Radenović, S.; Reshma, K. P.; Shukla, S. Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., Volume 8 (2015), pp. 1005-1013 | Zbl | DOI

[12] George, R.; Rajagopalan, R. Common fixed point results for \(\psi-\phi\) contractions in rectangular metric spaces, Bull. Math. Anal. Appl., Volume 5 (2013), pp. 44-52 | Zbl

[13] Bhaskar, T. Gnana; Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Volume 65 (2006), pp. 1379-1393

[14] Isık, H.; Türkoğlu, D. Common fixed points for ( \(\psi,\alpha,\beta\))-weakly contractive mappings in generalized metric spaces, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-6 | DOI | Zbl

[15] Kirk, W. A.; Shahzad, N. Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-9 | Zbl | DOI

[16] Lahiri, B. K.; P. Das Fixed point of a Ljubomir Ćirić’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen, Volume 61 (2002), pp. 589-594 | Zbl

[17] Lakshmikantham, V.; L. Ćirić Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., Volume 70 (2009), pp. 4341-4349

[18] Lakzian, H.; Samet, B. Fixed points for (\(\psi,\phi\))-weakly contractive mappings in generalized metric spaces, Appl. Math. Lett., Volume 25 (2012), pp. 902-906

[19] Rosa, V. La; Vetro, P. Common fixed points for \(\alpha-\psi-\phi\)-contractions in generalized metric spaces, Nonlinear Anal. Model. Control, Volume 19 (2014), pp. 43-54

[20] Roshan, J. R.; Parvaneh, V.; Kadelburg, Z.; H. Zoran New fixed point results in b-rectangular metric spaces, Nonlinear Anal. Model. Control, Volume 21 (2016), pp. 614-634 | DOI

[21] Samet, B. A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal. (Ruse), Volume 3 (2009), pp. 1265-1271

Cité par Sources :