FIXED POINT THEOREM OF KANNAN-TYPE MAPPINGS IN GENERALIZED FUZZY METRIC SPACES

محورهای موضوعی : فصلنامه ریاضی

Esmaeil Feizi ¹ (Bu-Ali Sina university Iran, Islamic Republic of)

تاریخ دریافت : 1395/01/27 تاریخ پذیرش : 1395/01/27 تاریخ انتشار : 1395/01/01

کلید واژه: fixed point, Generalized Fuzzy metric space, Kannan-type mappings, Generalized Kannan-type mappings,

چکیده مقاله :

Binayak et al in [1] proved a fixed point of generalized Kannan type-mappings in generalized Menger spaces. In this paper we extend gen- eralized Kannan-type mappings in generalized fuzzy metric spaces. Then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. Finally we present an example of our main result.

منابع و مأخذ:

Binayak S. Choudhury and Kirshnapada Das, Fixed point of generalized Kannan-type mappings in generalized menger spaces, Commun. Korean. Math. Soc., 24 (2009), No. 4,529-537.

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. Kaleva[3] R. Chugh and S. Kumar, Weakly compatible maps in generalized fuzzy metric spaces, J. Analysis. 10 (2002) 65-74.

Pratulanada Das and Lakshmi Kanta Dey, A fixed point theorem in generalized metric spaces, Soochow Journal of mathematics, No., 1 (2007) 33-39.

Z. K. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86 (1982) 74-95.

C. Dibari and C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math. 13(2005) 973-982.

A. George and P. Veeramani, On some results in metric spaces, Fuzzy Set and System., 64 (1994) 395-399.

M. Grabiec, Fixed point in fuzzy metric spaces, Fuzzy Set and System., 27 (1988) 385-389.

R. Kannan, Some result on fixed points, Bull. Calcutta Math. Soc., 60 (1968) 71-76.

I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika. 11 (1975) 336-344.

K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535-537.

P. V. Subrahmanyam, Completeness and xed points, Monatsh, Math. 80(1975) 325-330.

L. A. Zadeh, Fuzzy sets, Inform and Control, 8(1965) 338-353.