On a Fixed Point for Generalized Contractions in Generalized Metric Spaces

Lakzian and Samet (2010) studied some fixed-point results in generalized metric spaces in the sense of Branciari. In this paper, we study the existence of fixed-point results of mappings satisfying generalized weak contractive conditions in the framework of a generalized metric space in sense of Branciari. Our results modify and generalize the results of Laksian and Samet, as well as, our results generalize several well-known comparable results in the literature.

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

[2]  P. Das.  A FIXED POINT THEOREM ON A CLASS OF GENERALIZED METRIC SPACES , 2002 .

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

[4]  L. Kikina,et al.  On fixed point of a Ljubomir Ciric quasi-contraction mapping in generalized metric spaces , 2013 .

[5]  Bessem Samet,et al.  Fixed points for (Ψ, φ)-weakly contractive mappings in generalized metric spaces , 2012, Appl. Math. Lett..

[6]  L. Dey,et al.  POROSITY OF CERTAIN CLASSES OF OPERATORS IN GENERALIZED METRIC SPACES , 2009 .

[7]  FIXED POINT OF A LJUBOMIR CIRICS QUASI-CONTRACTIONMAPPING IN A GENERALIZED METRIC SPACE , 2002 .

[8]  L. Dey,et al.  Fixed point of contractive mappings in generalized metric spaces , 2009 .

[9]  A FIXED POINT THEOREM IN A GENERALIZED METRIC SPACE FOR MAPPINGS SATISFYING A CONTRACTIVE CONDITION OF INTEGRAL TYPE , 2009 .

[10]  ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES , 2009 .

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

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

[13]  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.

[14]  P. Das.  A FIXED POINT THEOREM IN A GENERALIZED METRIC SPACE , 2007 .

[15]  M. Arshad,et al.  KANNAN FIXED POINT THEOREM ON GENERALIZED METRIC SPACES , 2008 .

[16]  SOME RESULTS IN FIXED POINT THEORY CONCERNING GENERALIZED METRIC SPACES , 2009 .