Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces

Coincidence point and common fixed point results with the concept of generalized altering distance functions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. As an application, we study the existence of a common solution to a system of integral equations.

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

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

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

[4]  Ishak Altun,et al.  A common fixed point theorem on ordered metric spaces , 2012 .

[5]  Ismat Beg,et al.  Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces , 2009 .

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

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

[8]  Ismat Beg,et al.  FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION IN PARTIALLY ORDERED METRIC SPACES , 2009 .

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

[10]  Binayak S. Choudhury.  A common unique fixed point result in metric spaces involving generalised altering distances , 2005 .

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

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

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

[14]  Hemant Kumar Nashine,et al.  New fixed point theorems for mappings satisfying a generalized weakly contractive condition with weaker control functions , 2012 .

[15]  Simeon Reich,et al.  Some fixed point problems , 1974 .

[16]  Miloje Rajović,et al.  Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces , 2008 .

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

[18]  Hemant Kumar Nashine,et al.  Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations , 2012 .

[19]  Hassen Aydi,et al.  Coincidence and common fixed point results in partially ordered cone metric spaces and applications , 2011 .

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

[21]  Ravi P. Agarwal,et al.  Generalized contractions in partially ordered metric spaces , 2008 .

[22]  Alireza Amini-Harandi,et al.  A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations , 2010 .

[23]  Ishak Altun,et al.  Fixed Point Theorems for Generalized Weakly Contractive Condition in Ordered Metric Spaces , 2011 .

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

[25]  Hemant Kumar Nashine,et al.  Fixed point results for contractions involving generalized altering distances in ordered metric spaces , 2011 .

[26]  G. Jungck.  Compatible mappings and common fixed points , 1986 .

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

[28]  Q Zhang,et al.  FIXED POINT THEORY FOR PHI-WEAK CONTRACTIONS , 2009 .

[29]  Hemant Kumar Nashine,et al.  Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces , 2011, Math. Comput. Model..

[30]  Mujahid Abbas,et al.  Common Fixed Point Theorem of Two Mappings Satisfying a Generalized Weak Contractive Condition , 2009, Int. J. Math. Math. Sci..

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

[32]  J. S. W. Wong,et al.  On nonlinear contractions , 1969 .

[33]  Salvatore Sessa,et al.  Fixed point theorems by altering distances between the points , 1984, Bulletin of the Australian Mathematical Society.

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

[35]  Ravi P. Agarwal,et al.  Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces , 2003 .

[36]  Qingnian Zhang,et al.  Fixed point theory for generalized phi-weak contractions , 2009, Appl. Math. Lett..

[37]  B. C. Dhage.  CONDENSING MAPPINGS AND APPLICATIONS TO EXISTENCE THEOREMS FOR COMMON SOLUTION OF DIFFERENTIAL EQUATIONS , 1999 .

[38]  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..

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

[40]  Acharya Nagarjuna,et al.  Common Fixed Points Through Generalized Altering Distance Function , 2007 .

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

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