Common fixed points for (g, f) type maps in cone metric spaces

Abstract In this paper we study common fixed points for the self and non-self (g, f) type maps in cone metric spaces. Our main results are related to the cases when g is f quasi contraction in a sense of Das and Naik, and the cone need not be normal. These results generalize several well known comparable results in the literature.

[1]  Xian Zhang,et al.  Cone metric spaces and fixed point theorems of contractive mappings , 2007 .

[2]  K. M. Das,et al.  Common fixed-point theorems for commuting maps on a metric space , 1979 .

[3]  William A. Kirk,et al.  Fixed point theorems for set-valued mappings of contractive type , 1972 .

[4]  K. Deimling.  Nonlinear functional analysis , 1985 .

[5]  G. Jungck,et al.  Commuting Mappings and Fixed Points , 1976 .

[6]  Vladimir Rakocevic,et al.  Quasi-contraction on a cone metric space , 2009, Appl. Math. Lett..

[7]  M. A. Krasnoselʹskii,et al.  Geometrical Methods of Nonlinear Analysis , 1984 .

[8]  Naseer Shahzad,et al.  Some notes on fixed points of quasi-contraction maps , 2010, Appl. Math. Lett..

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

[10]  L. Ciric,et al.  A generalization of Banach’s contraction principle , 1974 .

[11]  Stojan Radenovic,et al.  Fixed point theorem for two non-self mappings in cone metric spaces , 2009, Comput. Math. Appl..

[12]  B. E. Rhoades,et al.  Assad-Kirk-Type Fixed Point Theorems for a Pair of Nonself Mappings on Cone Metric Spaces , 2009 .

[13]  V. Rakocević,et al.  Quasicontraction nonself-mappings on convex metric spaces and common fixed point theorems , 2005 .

[14]  Mujahid Abbas,et al.  Fixed and periodic point results in cone metric spaces , 2009, Appl. Math. Lett..

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

[16]  Ljiljana Gajic,et al.  On Ciric maps with a generalized contractive iterate at a point and Fisher's quasi-contractions in cone metric spaces , 2010, Appl. Math. Comput..

[17]  P. P. Zabrejko.  K-metric and K-normed linear spaces: survey. , 1997 .

[18]  Ljiljana Gajic,et al.  Pair of non-self-mappings and common fixed points , 2007, Appl. Math. Comput..

[19]  Stojan Radenovic,et al.  Remarks on "Quasi-contraction on a cone metric space" , 2009, Appl. Math. Lett..

[20]  Seiyed Mansour Vaezpour,et al.  Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces , 2008 .

[21]  K. Ng,et al.  Partially ordered topological vector spaces , 1973 .

[22]  G. Jungck,et al.  Common Fixed Point Theorems for Weakly Compatible Pairs on Cone Metric Spaces , 2009 .

[23]  Rhoades-type fixed-point theorems for a pair of nonself mappings , 2003 .

[24]  Vladimir Rakočević,et al.  Common fixed points for maps on cone metric space , 2008 .

[25]  S. Rezapour,et al.  Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings" , 2008 .

[26]  K. M. Das,et al.  Common fixed point theorems for commuting maps on metric spaces , 1979 .

[27]  Mujahid Abbas,et al.  Common fixed point results for noncommuting mappings without continuity in cone metric spaces , 2008 .

[28]  R. Tourky,et al.  Cones and duality , 2007 .

[29]  Pasquale Vetro,et al.  Common fixed points in cone metric spaces , 2007 .