ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES
Authors
Dorel Miheţ
 West University of Timişoara, Bv. V. Parvan 4, 300223, Timişoara, Romania..
Abstract
The concept of a generalized metric space, where the triangle
inequality has been replaced by a more general one involving four points, has
been recently introduced by Branciari. Subsequently, some classical metric
fixed point theorems have been transferred to such a space. The aim of this
note is to show that Kannan's fixed point theorem in a generalized metric space
is a consequence of the Banach contraction principle in a metric space.
Keywords
 Generalized metric space
 Torbitally complete
 Fixed point.
MSC
References

[1]
M. Akram, A. Siddiqui , A fixed point theorem for Acontractions on a class of generalized metric spaces, Korean J. Math. Sciences, 10 (2) (2003), 15.

[2]
A. Azam, M. Arshad , Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl. , 1 (1) (2008), 4548.

[3]
A. Branciari, A fixed point theorem of BanachCaccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (12) (2000), 3137.

[4]
Lb. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45(2) (1974), 267273.

[5]
P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sc., 9 (1) (2002), 2933.

[6]
P. Das, L. K. Dey, A fixed point theorem in a eneralized metric space, Soochow Journal of Mathematics , 33 (1) (2007), 3339.

[7]
B. K. Lahiri, P. Das, Fixed point of a Ljubomir Ćirić's quasicontraction mapping in a generalized metric space, Publ. Math. Debrecen, 61 (34) (2002), 589594.

[8]
R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 7176.

[9]
D. N. Sarknel, Banach's fixed point theorem implies Kannan's, Bull. Cal. Math. Soc., 91 (2) (1999), 143144.