JOURNAL BROWSE
Search
Advanced SearchSearch Tips
FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES
Choudhury, Binayak S.; Das, Krishnapada;
  PDF(new window)
 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
1.
Cyclic Coupled Fixed Point Result Using Kannan Type Contractions, Journal of Operators, 2014, 2014, 1  crossref(new windwow)
2.
Unique fixed points of p-cyclic kannan type probabilistic contractions, Bollettino dell'Unione Matematica Italiana, 2016  crossref(new windwow)
3.
Coupled Kannan-Type Coincidence Point Results in Partially Ordered Fuzzy Metric Spaces, Vietnam Journal of Mathematics, 2015, 43, 1, 105  crossref(new windwow)
4.
EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES, Communications of the Korean Mathematical Society, 2012, 27, 2, 265  crossref(new windwow)
 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 crossref(new window)

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 crossref(new window)

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

10.
R. Kannan, Some results on fixed point II, Amer. Math. Monthly 76 (1969), 405–408 crossref(new window)

11.
M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings Fixed Point Theory and Applications 2008 (2008), Article ID 649749 crossref(new window)

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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

20.
B. Sing and S. Jain, A fixed point theorem in Menger spaces through weak compatibility, J. Math. Anal. Appl. 301 (2005), no. 2, 439-448 crossref(new window)

21.
P. V. Subrahmanyam, Completeness and fixed points, Monatsh. Math. 80 (1975), 325-330 crossref(new window)