Some common coupled fixed point results in two S-metric spaces and applications to integral equations

Volume 9, Issue 6, pp 3527--3544 http://dx.doi.org/10.22436/jnsa.009.06.08

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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 S-metrics. 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.

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Keywords

• S-metric space
• contractive mappings
• coupled coincidence point
• coupled common fixed point
• mixed g-monotone property.

MSC

•  47H10
•  54H25

References

• [1] J. M. Afra, Fixed point type theorem in S-metric spaces, Middle-East J. Sci. Res., 22 (2014), 864-869.


• [2] J. M. Afra , Fixed point type theorem for weak contraction in S-metric spaces, Int. J. Res. Rev. Appl. Sci., 22 (2015), 11-14.


• [3] J. M. Afra, Double contraction in S-metric spaces , Int. J. Math. Anal., 9 (2015), 117-125.


• [4] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393.


• [5] P. Chouhan, N. Malviya, A common unique fixed point theorem for expansive type mappings in S-metric spaces, Int. Math. Forum, 8 (2013), 1287-1293.


• [6] B. C. Dhage , Generalized metric spaces and mappings with fixed point , Bull. Calcutta Math. Soc., 84 (1992), 329-336.


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


• [8] N. V. Dung, N. T. Hieu, S. Radojević, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28 (2014), 1885-1898.


• [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 S-metric spaces, Miskolc Math. Notes, 16 (2015), 181-194.


• [11] N. T. Hieu, N. T. Thanh Ly, N. V. Dung, A generalization of Ćirić quasi-contractions for maps on S-metric spaces, Thai J. Math., 13 (2015), 369-380.


• [12] J. K. Kim, S. Sedghi, N. Shobkolaei , Common fixed point theorems for the R-weakly commuting mappings in S-metric spaces, J. Comput. Anal. Appl., 19 (2015), 751-759.


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


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


• [15] M. U. Rahman, M. Sarwar, M. U. Rahman, Fixed point results of Altman integral type mappings in S-metric spaces, Int. J. Anal. Appl., 10 (2016), 58-63.


• [16] H. Raj, N. Hooda, Coupled fixed point theorems S-metric spaces with mixed g-monotone property, Int. J. Emerging Trends Eng. Dev., 4 (2014), 68-81.


• [17] H. Raj, N. Hooda, Coupled coincidence fixed point theorems in S-metric spaces, IOSR J. Math., 10 (2014), 59-64.


• [18] S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik, 66 (2014), 113-124.


• [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), 225-237.


• [20] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces , Mat. Vesnik, 64 (2012), 258-266.