Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces

Abstract In this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to Ciric (2009) [3] . An example is given to illustrate the usability of our results.

[1]  Bessem Samet,et al.  Coupled fixed point theorems for a generalized Meir–Keeler contraction in partially ordered metric spaces , 2010 .

[3]  B. Rhoades,et al.  A comparison of various definitions of contractive mappings , 1977 .

[4]  L. Ciric,et al.  Fixed point theorems for multi-valued contractions in complete metric spaces , 2008 .

[5]  A fixed point theorem for a multivalued non-self mapping , 1996 .

[6]  S. Nadler.  Multi-valued contraction mappings. , 1969 .

[7]  Stojan Radenovic,et al.  Generalized weak contractions in partially ordered metric spaces , 2010, Comput. Math. Appl..

[8]  Bessem Samet,et al.  Coupled fixed point, $F$-invariant set and fixed point of $N$-order , 2010 .

[9]  Juan J. Nieto,et al.  Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2005, Order.

[10]  Some generalizations of Mizoguchi-Takahashi’s fixed point theorem with new local constraints , 2007 .

[11]  S. Banach.  Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[12]  V. Lakshmikantham,et al.  Fixed point theorems in partially ordered metric spaces and applications , 2006 .

[13]  L. Ciric,et al.  Multi-valued nonlinear contraction mappings , 2009 .

[14]  COUPLED FIXED POINTS OF SET VALUED MAPPINGS IN PARTIALLY ORDERED METRIC SPACES , 2010 .

[15]  M. Abbas,et al.  Coupled Coincidence Point and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces with -Distance , 2010 .

[16]  J. Harjani,et al.  Fixed point theorems for mixed monotone operators and applications to integral equations , 2011 .

[17]  J. Harjani,et al.  Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations , 2010 .

[18]  Wataru Takahashi,et al.  Fixed point theorems for multivalued mappings on complete metric spaces , 1989 .

[19]  Bessem Samet,et al.  Coupled fixed point theorems in partially ordered ε-chainable Metric spaces , 2010 .

[20]  J. Harjani,et al.  Fixed point theorems for weakly contractive mappings in partially ordered sets , 2009 .

[21]  A COMMON FIXED POINT THEOREM FOR MULTIVALUED ´ CIRI ´ C TYPE MAPPINGS WITH NEW TYPE COMPATIBILITY , 2009 .

[22]  Hemant Kumar Nashine,et al.  Fixed point results for mappings satisfying (ψ,φ)-weakly contractive condition in partially ordered metric spaces , 2011 .

[23]  Binayak S. Choudhury,et al.  A coupled coincidence point result in partially ordered metric spaces for compatible mappings , 2010 .

[24]  B. E. Rhoades,et al.  Fixed point theorems in generalized partially ordered G-metric spaces , 2010, Math. Comput. Model..

[25]  Juan J. Nieto,et al.  Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2007 .

[26]  A. Ran,et al.  A fixed point theorem in partially ordered sets and some applications to matrix equations , 2003 .

[27]  Wei-Shih Du.  Coupled Fixed Point Theorems for Nonlinear Contractions Satisfied Mizoguchi-Takahashi's Condition in Quasiordered Metric Spaces , 2010 .

[28]  Juan J. Nieto,et al.  Fixed point theorems in ordered abstract spaces , 2007 .

[29]  Mihai Turinici,et al.  Abstract comparison principles and multivariable Gronwall-Bellman inequalities , 1986 .

[30]  V. Lakshmikantham,et al.  Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces , 2009 .

[31]  Donal O'Regan,et al.  Fixed point theorems for generalized contractions in ordered metric spaces , 2008 .