α−ψ−φ -contractive mappings in ordered partial b-metric spaces

In this paper, we introduce the concept of α-ψ-φ-contractive self mapping in complete ordered partial b−metric space, and we study the existence of fixed points for such mappings under some conditions. Presented theorems in this paper extend and generalize the results derived by Mustafa et al. in [17]. Some examples are given to illustrate the main results.

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

[2]  Suzuki type fixed point theorems for generalized multi-valued mappings in b-metric spaces , 2013 .

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

[4]  Erdal Karapinar,et al.  A generalized contraction principle with control functions on partial metric spaces , 2012, Comput. Math. Appl..

[5]  H. Nashine,et al.  A generalization of Banachs contraction principle for nonlinear contraction in a partial metric space , 2012 .

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

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

[8]  Bessem Samet,et al.  Fixed point theorems for α–ψ-contractive type mappings , 2012 .

[9]  Hukmi Kiziltunç,et al.  On Some Well Known Fixed Point Theorems in b-Metric Spaces , 2013 .

[10]  Unique common fixed point theorems on partial metric spaces , 2014 .

[11]  Thabet Abdeljawad,et al.  Banach contraction principle for cyclical mappings on partial metric spaces , 2011, 1112.5891.

[12]  A fixed point theorem for set-valued quasicontractions in b-metric spaces , 2014 .

[13]  M. Imdad,et al.  Common fixed point theorems under rational contractions in complex valued metric spaces , 2015 .

[14]  R. Agarwal,et al.  A note on ‘Coupled fixed point theorems for α-ψ-contractive-type mappings in partially ordered metric spaces’ , 2013, Fixed Point Theory and Applications.

[15]  Thabet Abdeljawad.  Meir-Keeler ɑ-contractive fixed and common fixed point theorems , 2013 .

[16]  C. Vetro,et al.  Common fixed points of mappings satisfying implicit relations in partial metric spaces , 2013 .

[17]  Vahid Parvaneh,et al.  Some common fixed point results in ordered partial b-metric spaces , 2013 .

[18]  Bessem Samet,et al.  Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications , 2012 .

[19]  Naseer Shahzad,et al.  On fixed points of α-ψ-contractive multifunctions , 2012 .

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

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

[22]  Aurora Fernández-León,et al.  Best proximity points for cyclic mappings , 2011 .

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