Strong Common Coupled Fixed Point Result in Fuzzy Metric Spaces

Coupled fixed point problems have attracted large attention in recent times. In this paper we have proved a fuzzy coupled fixed point result. Precisely, we have defined the concept of strong coupled fixed point and have established the existence of a unique common strong coupled fixed point for two mappings on fuzzy metric spaces which satisfy certain contractive inequality. The main theorem has a corollary and is supported with an example. The example demonstrates that the theorem properly contains its corollary.

[1]  Xin-Qi Hu,et al.  Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces , 2011 .

[2]  V. Lakshmikantham,et al.  Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces , 2009 .

[3]  Dorel Mihet,et al.  On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces , 2007, Fuzzy Sets Syst..

[4]  H. P. Masiha,et al.  Some Coupled Fixed Point Theorems in Cone Metric Spaces , 2009 .

[5]  Xing-Hua Zhu,et al.  Common coupled fixed point results for probabilistic f -contractions in Menger spaces , 2011 .

[6]  Salvador Romaguera,et al.  The Hausdor$ fuzzy metric on compact sets , 2004 .

[7]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[8]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[9]  Hemant Kumar Nashine,et al.  Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces , 2011, Comput. Math. Appl..

[10]  Binayak S. Choudhury,et al.  Coupled fixed point results in generalized metric spaces , 2011, Math. Comput. Model..

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

[12]  Ivan Kramosil,et al.  Fuzzy metrics and statistical metric spaces , 1975, Kybernetika.

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

[14]  Erdal Karapinar,et al.  Couple fixed point theorems for nonlinear contractions in cone metric spaces , 2010, Comput. Math. Appl..

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

[16]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[17]  Ishak Altun,et al.  Coupled fixed point theorems for contractions in fuzzy metric spaces , 2010 .

[18]  A. Razani,et al.  A contraction theorem in fuzzy metric spaces , 2005 .

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

[20]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[21]  L. Ciric Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces , 2009 .

[22]  Nguyen Van Luong,et al.  Coupled fixed points in partially ordered metric spaces and application , 2011 .