Some common coupled fixed point results in two Smetric spaces and applications to integral equations

1703
Downloads

3156
Views
Authors
Liya Liu
 Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.
Feng Gu
 Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.
Abstract
The purpose of this paper is to prove some new coupled common fixed point theorems for mappings
defined on a set equipped with two Smetrics. We also provide illustrative examples in support of our new
results. Meantime, we give an existence and uniqueness theorem of solution for a class of nonlinear integral
equations by using the obtained result.
Share and Cite
ISRP Style
Liya Liu, Feng Gu, Some common coupled fixed point results in two Smetric spaces and applications to integral equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 35273544
AMA Style
Liu Liya, Gu Feng, Some common coupled fixed point results in two Smetric spaces and applications to integral equations. J. Nonlinear Sci. Appl. (2016); 9(6):35273544
Chicago/Turabian Style
Liu, Liya, Gu, Feng. "Some common coupled fixed point results in two Smetric spaces and applications to integral equations." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 35273544
Keywords
 Smetric space
 contractive mappings
 coupled coincidence point
 coupled common fixed point
 mixed gmonotone property.
MSC
References

[1]
J. M. Afra, Fixed point type theorem in Smetric spaces, MiddleEast J. Sci. Res., 22 (2014), 864869.

[2]
J. M. Afra , Fixed point type theorem for weak contraction in Smetric spaces, Int. J. Res. Rev. Appl. Sci., 22 (2015), 1114.

[3]
J. M. Afra, Double contraction in Smetric spaces , Int. J. Math. Anal., 9 (2015), 117125.

[4]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 13791393.

[5]
P. Chouhan, N. Malviya, A common unique fixed point theorem for expansive type mappings in Smetric spaces, Int. Math. Forum, 8 (2013), 12871293.

[6]
B. C. Dhage , Generalized metric spaces and mappings with fixed point , Bull. Calcutta Math. Soc., 84 (1992), 329336.

[7]
N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered Smetric spaces, Fixed Point Theory Appl., 2013 (2013), 17 pages.

[8]
N. V. Dung, N. T. Hieu, S. Radojević, Fixed point theorems for gmonotone maps on partially ordered Smetric spaces, Filomat, 28 (2014), 18851898.

[9]
F. Gu, Z. Yang, Some new common fixed point results for three pairs of mappings in generalized metric spaces, Fixed point Theory Appl., 2013 (2013), 21 pages.

[10]
V. Gupta, R. Deep, Some coupled fixed point theorems in partially ordered Smetric spaces, Miskolc Math. Notes, 16 (2015), 181194.

[11]
N. T. Hieu, N. T. Thanh Ly, N. V. Dung, A generalization of Ćirić quasicontractions for maps on Smetric spaces, Thai J. Math., 13 (2015), 369380.

[12]
J. K. Kim, S. Sedghi, N. Shobkolaei , Common fixed point theorems for the Rweakly commuting mappings in Smetric spaces, J. Comput. Anal. Appl., 19 (2015), 751759.

[13]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 43414349.

[14]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289297.

[15]
M. U. Rahman, M. Sarwar, M. U. Rahman, Fixed point results of Altman integral type mappings in Smetric spaces, Int. J. Anal. Appl., 10 (2016), 5863.

[16]
H. Raj, N. Hooda, Coupled fixed point theorems Smetric spaces with mixed gmonotone property, Int. J. Emerging Trends Eng. Dev., 4 (2014), 6881.

[17]
H. Raj, N. Hooda, Coupled coincidence fixed point theorems in Smetric spaces, IOSR J. Math., 10 (2014), 5964.

[18]
S. Sedghi, N. V. Dung, Fixed point theorems on Smetric spaces, Mat. Vesnik, 66 (2014), 113124.

[19]
S. Sedghi, K. P. R. Rao, N. Shobe, Common fixed point theorems for six weakly compatible mappings in D*metric spaces, Int. J. Math. Sci., 6 (2007), 225237.

[20]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in Smetric spaces , Mat. Vesnik, 64 (2012), 258266.