Browse > Article
http://dx.doi.org/10.4134/CKMS.2009.24.4.529

FIXED POINTS OF GENERALIZED KANNAN TYPE MAPPINGS IN GENERALIZED MENGER SPACES  

Choudhury, Binayak S. (DEPARTMENT OF MATHEMATICS BENGAL ENGINEERING AND SCIENCES UNIVERSITY)
Das, Krishnapada (DEPARTMENT OF MATHEMATICS BENGAL ENGINEERING AND SCIENCES UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.4, 2009 , pp. 529-537 More about this Journal
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; $\Psi$-function;
Citations & Related Records

Times Cited By SCOPUS : 3
연도 인용수 순위
  • Reference
1 B. S. Choudhury and K. P. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica, English Series 24 (2008), 1379–1386   DOI
2 B. S. Choudhury and K. P. Das, Banach contraction mapping principle in generalized Menger spaces, (Communicated)
3 P. Das, A fixed point theorem on a class of generalized metric space, Korean J. Math. Soc. 9 (2002), no. 1, 29–33
4 R. Kannan, Some results on fixed point II, Amer. Math. Monthly 76 (1969), 405–408   DOI   ScienceOn
5 R. Kannan, Some results on fixed point, Bull. Cal. Math. Soc. 60 (1968), 71–76
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   DOI   ScienceOn
8 O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, 2001
9 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   DOI   ScienceOn
10 P. V. Subrahmanyam, Completeness and fixed points, Monatsh. Math. 80 (1975), 325-330   DOI
11 A. Razani and K. Fouladgar, Extension of contractive maps in the Menger probabilistic metric space, Chaos, Solitons and Fractals 34 (2007), 1724–1731   DOI   ScienceOn
12 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
13 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   과학기술학회마을
14 B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland, Amsterdam, 1983
15 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   DOI
16 M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings Fixed Point Theory and Applications 2008 (2008), Article ID 649749   DOI
17 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
18 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
19 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
20 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   DOI
21 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   DOI   ScienceOn