Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results.

[1]  Z. Kadelburg,et al.  Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces , 2014, Journal of Inequalities and Applications.

[2]  Branislav Z. Popovic,et al.  C-class functions with new approach on coincidence point results for generalized $$(\psi ,\varphi )$$(ψ,φ)-weakly contractions in ordered b-metric spaces , 2016, SpringerPlus.

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

[4]  Shujun Jiang,et al.  A note on ‘Some fixed point theorems for generalized contractive mappings in complete metric spaces’ , 2016, Fixed Point Theory and Applications.

[5]  Vahid Parvaneh,et al.  Existence of a tripled coincidence point in ordered Gb-metric spaces and applications to a system of integral equations , 2013, Journal of Inequalities and Applications.

[6]  Z. Kadelburg,et al.  Fixed point results in generalized metric spaces without Hausdorff property , 2014 .

[7]  Abdolrahman Razani,et al.  Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Ordered b-Metric Spaces , 2014, J. Appl. Math..

[8]  A. H. Ansari,et al.  Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions , 2014, Journal of Inequalities and Applications.

[9]  W. Sintunavarat,et al.  Fixed point result and applications on a b-metric space endowed with an arbitrary binary relation , 2013 .

[10]  Z. Kadelburg,et al.  b2-Metric spaces and some fixed point theorems , 2014 .

[11]  Tomonari Suzuki,et al.  Generalized Metric Spaces Do Not Have the Compatible Topology , 2014 .

[12]  Bessem Samet,et al.  Discussion on "A fixed point theorem of Banach--Caccioppoli type on a class of generalized metric spaces" by A. Branciari , 2010, Publicationes Mathematicae Debrecen.

[13]  Zead Mustafa,et al.  Some common fixed point results of graphs on b -metric space , 2016 .

[14]  Reny George,et al.  Rectangular b-metric space and contraction principles , 2015 .

[15]  I. Ramabhadra Sarma,et al.  CONTRACTIONS OVER GENERALIZED METRIC SPACES , 2009 .

[16]  A. Ivanov.  Fixed points of mappings of metric spaces , 1979 .

[18]  Vahid Parvaneh,et al.  Some fixed point theorems for generalized contractive mappings in complete metric spaces , 2015 .

[19]  S. Kakutani.  A generalization of Brouwer’s fixed point theorem , 1941 .

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

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

[22]  Bessem Samet,et al.  A new generalization of the Banach contraction principle , 2014, Journal of Inequalities and Applications.

[23]  A Branciari,et al.  A fixed point theorem of Banach--Caccioppoli type on a class of generalized metric spaces , 2000, Publicationes Mathematicae Debrecen.

[24]  Z. Kadelburg,et al.  ON GENERALIZED METRIC SPACES: A SURVEY , 2014 .

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

[26]  Vahid Parvaneh,et al.  New fixed point results in b-rectangular metric spaces , 2016 .

[27]  E. Karapınar,et al.  Fixed Points of Generalized -Suzuki Type Contraction in Complete -Metric Spaces , 2015 .

[28]  Hassen Aydi,et al.  Fixed points for generalized (α,ψ)-contractions on generalized metric spaces , 2014, Journal of Inequalities and Applications.

[29]  Kim C. Border,et al.  Fixed point theorems with applications to economics and game theory: Fixed point theorems for correspondences , 1985 .