# ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES

Volume 2, Issue 2, pp 92-96 Publication Date: May 15, 2009
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### 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The concept of a generalized metric space, where the triangle inequality has been replaced by a more general one involving four points, has been recently introduced by Branciari.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
• T-orbitally complete
• Fixed point.

•  47H10
•  54H25

### References

• [1] M. Akram, A. Siddiqui , A fixed point theorem for A-contractions on a class of generalized metric spaces, Korean J. Math. Sciences, 10 (2) (2003), 1-5.

• [2] A. Azam, M. Arshad , Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl. , 1 (1) (2008), 45-48.

• [3] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (1-2) (2000), 31-37.

• [4] Lb. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45(2) (1974), 267-273.

• [5] P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sc., 9 (1) (2002), 29-33.

• [6] P. Das, L. K. Dey, A fixed point theorem in a eneralized metric space, Soochow Journal of Mathematics , 33 (1) (2007), 33-39.

• [7] B. K. Lahiri, P. Das, Fixed point of a Ljubomir Ćirić's quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen, 61 (3-4) (2002), 589-594.

• [8] R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.

• [9] D. N. Sarknel, Banach's fixed point theorem implies Kannan's, Bull. Cal. Math. Soc., 91 (2) (1999), 143-144.