FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES

- Journal title : Communications of the Korean Mathematical Society
- Volume 24, Issue 4, 2009, pp.529-537
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2009.24.4.529

Title & Authors

FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES

Choudhury, Binayak S.; Das, Krishnapada;

Choudhury, Binayak S.; Das, Krishnapada;

Abstract

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

Keywords

generalized Menger space;fixed point;Kannan type mapping;-function;

Language

English

Cited by

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References

1.

A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), no. 1-2, 31–37

2.

B. S. Choudhury, A unique common fixed point theorem for a sequence of self-mappings in Menger Spaces, Bull. Korean Math. Soc. 37 (2000), no. 3, 569–573

3.

B. S. Choudhury and K. P. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica, English Series 24 (2008), 1379–1386

4.

B. S. Choudhury and K. P. Das, Banach contraction mapping principle in generalized Menger spaces, (Communicated)

5.

P. Das, A fixed point theorem on a class of generalized metric space, Korean J. Math. Soc. 9 (2002), no. 1, 29–33

6.

P. Das and L. K. Dey, A fixed point theorem in a generalized metric space, Soochow J. Math. 33 (2007), no. 1, 33–39

7.

J. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal. 70 (2009), no. 1, 184–193

8.

O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001

9.

R. Kannan, Some results on fixed point, Bull. Cal. Math. Soc. 60 (1968), 71–76

11.

M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings Fixed Point Theory and Applications 2008 (2008), Article ID 649749

12.

M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings II, Bull. Kyushu Inst. Tech. Pure Appl. Math. (2008), no. 55, 1–13

13.

I. Kubiaczyk and S. Sharma, Some common fixed point theorems in Menger space under strict contractive conditions, Southeast Asian Bull. Math. 32 (2008), 117–124

14.

B. K. Lahiri and P. Das, Fixed point of a Ljubomir Ciric's quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen 61 (2002), no. 3-4, 589–594

15.

A. Razani and K. Fouladgar, Extension of contractive maps in the Menger probabilistic metric space, Chaos, Solitons and Fractals 34 (2007), 1724–1731

16.

P. K. Saha and R. Tiwari, An alternative proof of Kannan's fixed point theorem in generalized metric space, News Bull. Cal. Math. Soc. 31 (2008), 15–18

17.

B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland, Amsterdam, 1983

18.

V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on PM space, Math. Sys. Theory 6 (1972), no. 2, 97-100

19.

Y. Shi, L. Ren, and X. Wang, The extension of fixed point theorems for set valued mapping, J. Appl. Math. & Computing 13 (2003), no. 1-2, 277-286