Fixed point of generalized weakly contractive mappings in ordered partial metric spaces

In this article, we prove some fixed point results for generalized weakly contractive mappings defined on a partial metric space. We provide some examples to validate our results. These results unify, generalize and complement various known comparable results from the current literature.AMS Classification 2010: 47H10; 54H25; 54E50.

[1]  Qingnian Zhang,et al.  Fixed point theory for generalized'-weak contractions , 2009 .

[2]  M. Noorani,et al.  Fixed Point Results in Quasi-Cone Metric Spaces , 2013 .

[3]  Erdal Karapinar,et al.  Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces , 2011 .

[4]  Bidyut Kumar Guha Thakurta,et al.  Some generating functions of Laguerre polynomials , 1987 .

[5]  Suliman Al-Homidan,et al.  Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory , 2008 .

[6]  Binayak S. Choudhury,et al.  A Generalisation of Contraction Principle in Metric Spaces , 2008 .

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

[8]  Hassen Aydi,et al.  SOME FIXED POINT RESULTS IN ORDERED PARTIAL METRIC SPACES , 2011, 1103.3680.

[9]  Ishak Altun,et al.  SOME FIXED POINT THEOREMS ON DUALISTIC PARTIAL METRIC SPACES , 2008 .

[10]  S. G. Matthews,et al.  Partial Metric Topology , 1994 .

[11]  Ishak Altun,et al.  Generalized contractions on partial metric spaces , 2010 .

[12]  Oscar Valero,et al.  On Banach fixed point theorems for partial metric spaces , 2005 .

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

[14]  Salvador Romaguera,et al.  Partial metric monoids and semivaluation spaces , 2005 .

[15]  M. O. Olatinwo Coupled fixed point theorems in cone metric spaces , 2011 .

[16]  Salvador Romaguera,et al.  A Kirk Type Characterization of Completeness for Partial Metric Spaces , 2009 .

[17]  Hassen Aydi Coincidence and Common Fixed Point Results for Contraction Type Maps in Partially Ordered Metric Spaces , 2011 .

[18]  Michael A. Bukatin,et al.  Partial Metrics and Co-continuous Valuations , 1998, FoSSaCS.

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

[20]  B. Rhoades,et al.  Some theorems on weakly contractive maps , 2001 .

[21]  S. Romaguera,et al.  -Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps , 2011 .

[22]  Mujahid Abbas,et al.  Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces , 2012, Math. Comput. Model..

[23]  Michel P. Schellekens,et al.  The correspondence between partial metrics and semivaluations , 2004, Theor. Comput. Sci..

[24]  Ovidiu Popescu,et al.  Fixed points for (psi, phi)-weak contractions , 2011, Appl. Math. Lett..

[25]  Oscar Valero,et al.  Banach's Fixed Point Theorem for Partial Metric Spaces , 2004 .

[26]  Ishak Altun,et al.  Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces , 2011 .

[27]  Ishak Altun,et al.  Some Fixed Point Theorems on Ordered Metric Spaces and Application , 2010 .

[28]  Adrian Petruşel,et al.  Fixed point theorems in ordered L-spaces , 2005 .

[29]  Stojan Radenovic,et al.  Common fixed points of four maps in partially ordered metric spaces , 2011, Appl. Math. Lett..

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

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

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

[33]  Ya. I. Alber,et al.  Principle of weakly contractive maps in Hilbert spaces , 1997 .

[34]  Mujahid Abbas,et al.  Fixed point results for generalized cyclic contraction mappings in partial metric spaces , 2012 .

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

[36]  Fixed Point Results in Quasimetric Spaces , 2011 .

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

[38]  A. Branciari,et al.  A FIXED POINT THEOREM FOR MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE , 2002 .

[39]  Ralph Kopperman,et al.  Partial Metric Spaces , 1992, Am. Math. Mon..