Surveys in Mathematics and its Applications

ISSN1842-6298 (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. ChoudhuryDepartment of Mathematics Bengal Engineering and Science University P.O.- B. Garden, Shibpur, Howrah - 711103, West Bengal, INDIA. e-mail: binayak12@yahoo.co.in

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