Some common fixed point results in ordered partial b-metric spaces

In this paper, we introduce a modified version of ordered partial b-metric spaces. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Using this lemma, we prove some fixed point and common fixed point results for (ψ,φ)-weakly contractive mappings in the setup of ordered partial b-metric spaces. Finally, examples are presented to verify the effectiveness and applicability of our main results.MSC: 47H10, 54H25.

[1]  Zoran Kadelburg,et al.  Fixed point results under various contractive conditions in partial metric spaces , 2013 .

[2]  Hassen Aydi.  Coupled Fixed Point Results in Ordered Partial Metric Spaces , 2012 .

[3]  Mohamed A. Khamsi,et al.  Remarks on Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings , 2010 .

[4]  Ishak Altun,et al.  Fixed point and common fixed point theorems on ordered cone metric spaces , 2010, Appl. Math. Lett..

[5]  Erdal Karapinar,et al.  Fixed point theory for cyclic (ϕ - ψ)-contractions , 2011 .

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

[7]  Mujahid Abbas,et al.  Common fixed points of almost generalized contractive mappings in ordered metric spaces , 2011, Appl. Math. Comput..

[8]  M. Khamsi,et al.  KKM mappings in metric type spaces , 2010 .

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

[10]  Z. Kadelburg,et al.  Common Fixed Point Results in Metric-Type Spaces , 2010 .

[11]  Hassen Aydi.  COMMON FIXED POINT RESULTS FOR MAPPINGS SATISFYING (PSI, PHI) -WEAK CONTRACTIONS IN ORDERED PARTIAL METRIC SPACES , 2012 .

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

[13]  Mujahid Abbas,et al.  Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces , 2014 .

[14]  Bhagwati Prasad,et al.  Some coincidence theorems and stability of iterative procedures , 2008, Comput. Math. Appl..

[15]  Hassen Aydi,et al.  A fixed point theorem for set-valued quasi-contractions in b-metric spaces , 2012, Fixed Point Theory and Applications.

[16]  M. Boriceanu.  FIXED POINT THEORY FOR MULTIVALUED GENERALIZED CONTRACTION ON A SET WITH TWO b-METRICS , 2009 .

[17]  Vahid Parvaneh,et al.  Common fixed points of almost generalized (ψ,φ)s-contractive mappings in ordered b-metric spaces , 2013 .

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

[19]  Stojan Radenovic,et al.  Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces , 2013, Math. Comput. Model..

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

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

[22]  S. Czerwik,et al.  Nonlinear set-valued contraction mappings in b-metric spaces , 1998 .

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

[24]  S. Moradi,et al.  A COMMON FIXED POINT FOR WEAK -CONTRACTIONS ON b-METRIC SPACES , 2012 .

[25]  Mădălina Păcurar,et al.  Fixed point theory for cyclic φ-contractions , 2010 .

[26]  Vahid Parvaneh,et al.  Common fixed points of almost generalized (ψ,φ)s(ψ,φ)ssψ , 2013 .

[27]  Ishak Altun,et al.  Common fixed point of mappings satisfying almost generalized (S, T)-contractive condition in partially ordered partial metric spaces , 2012, Appl. Math. Comput..

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

[29]  S. Czerwik,et al.  Contraction mappings in $b$-metric spaces , 1993 .

[30]  W. Shatanawi,et al.  Common fıxed points of almost generalized (ψ, ϕ)-contractive mappings in ordered metric spaces , 2012 .

[31]  Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations , 2013 .

[32]  Wasfi Shatanawi,et al.  Some Coincidence Point Theorems for Nonlinear Contraction in Ordered Metric Spaces , 2011 .

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

[34]  Masood Hussain Shah,et al.  KKM mappings in cone b-metric spaces , 2011, Comput. Math. Appl..

[35]  M. Abbas,et al.  Common fixed point of four maps in b−metric spaces , 2014 .

[36]  Z. Kadelburg,et al.  Suzuki-type fixed point results in metric type spaces , 2012 .

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

[38]  Stojan Radenovic,et al.  Common fixed point results for four mappings satisfying almost generalized (S, T)-contractive condition in partially ordered metric spaces , 2012, Appl. Math. Comput..

[39]  Satish Shukla,et al.  Partial b-Metric Spaces and Fixed Point Theorems , 2014 .

[40]  Z. Kadelburg,et al.  SOME RESULTS ON WEAKLY CONTRACTIVE MAPS , 2012 .

[41]  Dragan Doric,et al.  Common fixed point for generalized (psi, phi)-weak contractions , 2009, Appl. Math. Lett..