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 its applications, Tome 8 (2015) no. 4, p. 285-300.

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

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.
DOI : 10.22436/jnsa.008.04.01
Classification : 47H10, 54H25
Keywords: partially ordered set, quadruple coincidence, quadruple fixed point, G-metric space, mixed g-monotone property.

Chen, Jianhua 1 ; Huang, Xianjiu 1

1 Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China
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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 its applications, Tome 8 (2015) no. 4, p. 285-300. doi : 10.22436/jnsa.008.04.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.04.01/

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

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

[3] Chugh, R.; Kadian, T.; Rani, A.; Rhoades, B. E. Property P in G-metric spaces , Fixed Point Theory Appl., Volume 2010 (2012), pp. 1-12

[4] Karapınar, E.; Kumam, P.; Merhan, I. Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-13

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

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

[7] Karapınar, E. Quadruple fixed point theorems for weak \(\phi\)-contractions , ISRN Math. Anal., Volume 2011 (2011), pp. 1-15

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

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

[10] Karapınar, E.; Shatanawi, W.; Mustafa, Z. Quadruple fixed point theorems under nonlinear contractive conditions in partially ordered metric spaces, J. Appl. Math., Article ID 951912, (2012), pp. 1-17

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

[12] Liu, X. L. Quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-18

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

[14] Mustafa, Z.; Shatanawi, W.; M. Bataineh Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., Volume 2009 (2009), pp. 1-10

[15] Mustafa, Z.; Sims, B. Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., Volume 2009 (2009), pp. 1-10

[16] Mustafa, Z.; Aydi, H.; Karapınar, E. Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric space, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-19

[17] Mustafa, Z.; Obiedat, H.; F. Awawdeh Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., Volume 2008 (2008), pp. 1-12

[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., Volume 2012 (2012), pp. 1-22

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

[20] W. Shatanawi Fixed point theory for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces , Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-9

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