# Quadruple fixed point theorems under ($\varphi,\psi$)-contractive conditions in partially ordered $G$-metric spaces with mixed $g$-monotone property

Volume 8, Issue 4, pp 285--300
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### Authors

Jianhua Chen - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China. Xianjiu Huang - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.

### Abstract

In this paper, we prove some quadruple coincidence and quadruple fixed point theorems for ($\varphi,\psi$)-contractive type mappings in partially ordered G-metric spaces with mixed g-monotone property. The results on fixed point theorems are generalizations of some results obtained by Mustafa [Z. Mustafa, Fixed Point Theory Appl., 2012 (2012), 22 pages]. We also give an example to support our results.

### Share and Cite

##### ISRP Style

Jianhua Chen, Xianjiu Huang, Quadruple fixed point theorems under ($\varphi,\psi$)-contractive conditions in partially ordered $G$-metric spaces with mixed $g$-monotone property, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 4, 285--300

##### AMA Style

Chen Jianhua, Huang Xianjiu, Quadruple fixed point theorems under ($\varphi,\psi$)-contractive conditions in partially ordered $G$-metric spaces with mixed $g$-monotone property. J. Nonlinear Sci. Appl. (2015); 8(4):285--300

##### Chicago/Turabian Style

Chen, Jianhua, Huang, Xianjiu. "Quadruple fixed point theorems under ($\varphi,\psi$)-contractive conditions in partially ordered $G$-metric spaces with mixed $g$-monotone property." Journal of Nonlinear Sciences and Applications, 8, no. 4 (2015): 285--300

### Keywords

• partially ordered set
• G-metric space
• mixed g-monotone property.

•  47H10
•  54H25

### References

• [1] H. Aydi, B. Damjanović, B. Samet, W. Shatanawi , Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. Comput. Modelling, 54 (2010), 2443-2450.

• [2] V. Bernde , Coupled fixed point theorems for $\phi$-contractive mixed monotone mappings in partially ordered metric spaces, Nonliner Anal., 75 (2012), 3218-3228.

• [3] R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces , Fixed Point Theory Appl., 2010 (2012), 12 pages.

• [4] E. Karapınar, P. Kumam, I. Merhan, Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 13 pages.

• [5] E. Karapınar, N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Comput. Math. Appl., 64 (2012), 1839-1848.

• [6] E. Karapınar , Quartet fixed point for nonlinear contraction , http://arxiv.org/abs/1106.5472 , ()

• [7] E. Karapınar, Quadruple fixed point theorems for weak $\phi$-contractions , ISRN Math. Anal., 2011 (2011), 15 pages.

• [8] E. Karapınar, V. Berinde, Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces, Banach J. Math. Anal., 6 (2012), 74-89.

• [9] E. Karapınar , A new quartet fixed point theorem for nonlinear contractions, JP J. Fixed Point Theory Appl., 6 (2011), 119-135.

• [10] E. Karapınar, W. Shatanawi, Z. Mustafa, Quadruple fixed point theorems under nonlinear contractive conditions in partially ordered metric spaces, J. Appl. Math., Article ID 951912, , (2012), 17 pages.

• [11] N. V. Luong, N. X. Thuan, Coupled fixed point theorems in partially ordered G-metric spaces, Math. Comput. Modelling, 55 (2012), 1601-1609.

• [12] X. L. Liu, Quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property, Fixed Point Theory Appl., 2013 (2013), 18 pages.

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

• [14] Z. Mustafa, W. Shatanawi, M. Bataineh , Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., 2009 (2009), 10 pages.

• [15] Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., 2009 (2009), 10 pages.

• [16] Z. Mustafa, H. Aydi, E. Karapınar, Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric space, Fixed Point Theory Appl., 2012 (2012), 19 pages.

• [17] Z. Mustafa, H. Obiedat, F. Awawdeh , Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008 (2008), 12 pages.

• [18] Z. Mustafa , Mixed g-monotone property and quadruple fixed point theorems in partiallly ordered G-metric spaces using ( $\phi-\psi$ ) contractions , Fixed Point Theory Appl., 2012 (2012), 22 pages.

• [19] H. K. Nashine, Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 5 (2012), 1-13.

• [20] W. Shatanawi , Fixed point theory for contractive mappings satisfying $\Phi$-maps in G-metric spaces , Fixed Point Theory Appl., 2010 (2010), 9 pages.