Quadruple Fixed Point Results in Ordered Generalized Metric Spaces


  • Sagar Institute of Science, Technology and Research, Department of Engineering Mathematics, Bhopal, India


In this article we prove quadrupled fixed point results for a mixed monotone property satisfying nonlinear contraction in a partially ordered G-metric space. Also some examples are given in support of our result.


Quadrupled Fixed Points, Mixed Monotone Property, G-Metric Space, Partially Ordered Set.

Subject Discipline

Mathematical Sciences

Full Text:


M. Abbas and B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalised metric spaces, Appl. Math. Comput., 215, (2009), 262–269.

M. Abbas, Talat Nazir and Stojan Radenovic, Some periodic point results in generalized metric spaces, Appl.Math. Comput., 217 (2010), 4094–4099.

V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal, 74(15), (2011), 4889–4897.

E. Karapiner, Quadruple Fixed Point Theorems for Weak φ- Contraction, ISRN Math. Anal., (2011), ID 989423, 15 pages, doi:10.5402/2011/989423.

Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, University of Newcastle, Newcastle, UK, 2005.

Z. Mustafa, W. Shatanawi and M. Bataineh, Fixed point theorems on uncomplete Gmetric spaces, J. Math. Stat. 4(4), (2008), 196–201.

Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point result in G-metric spaces, Int. J. Math. Math. Sci., 2009(2009), Article ID 283028, 10 pages.

Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proc. Int. Conf. on Fixed Point Theor. Appl., Valencia, Spain, July 2003, 189–198.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7(2), (2006), 289–297.

Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric space, Fixed Point Theory Appl., 2009(2009), Article ID 917175, pages 10.

J. J. Nieto and R. Rodrguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22(3), (2005), 223–239.

B. Samet and C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal., 1(2), (2010), 46–56.

W. Shatanawi, Fixed point theory for contractive mappings satisfying - maps in Gmetric spaces, Fixed Point Theory Appl., 2010(2010), Article ID 181650, 9 pages.

W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., 60, (2010). 2508–2515.


  • There are currently no refbacks.