Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 4 (2009), 41 -- 52

SOME FIXED POINT RESULTS IN MENGER SPACES USING A CONTROL FUNCTION

P.N. Dutta, Binayak S. Choudhury and Krishnapada Das

Abstract. Here we prove a probabilistic contraction mapping principle in Menger spaces. This is in line with research in fixed point theory using control functions which was initiated by Khan et al. [Bull. Austral. Math. Soc., 30(1984), 1-9] in metric spaces and extended by Choudhury et al. [Acta Mathematica Sinica, 24(8) (2008), 1379-1386] in probabilistic metric spaces. An example has also been constructed.

2000 Mathematics Subject Classification: 54H25; 54E70.
Keywords: Menger space; p-convergence; Φ-function; fixed point.

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P.N. Dutta
Department of Mathematics
Government College of Engineering and Ceramic Technology,
73 A.C. Banergee Lane , Kolkata - 700010,
West Bengal, INDIA.
e-mail: prasanta_dutta1@yahoo.co.in


Binayak S. Choudhury
Department of Mathematics
Bengal Engineering and Science University
P.O.- B. Garden, Shibpur, Howrah - 711103,
West Bengal, INDIA.
e-mail: binayak12@yahoo.co.in


Krishnapada Das
Department of Mathematics,
Bengal Engineering and Science University, Shibpur
P.O.- B. Garden, Shibpur, Howrah - 711103,
West Bengal, INDIA.
e-mail: kestapm@yahoo.co.in

http://www.utgjiu.ro/math/sma