• ON A COMMON FIXED POINT THEOREM FOR FOUR SELF MAPS ON A MENGER SPACE

Abstract

Rashwan and Hedaer [3] proved a fixed point theorem on a Menger space, under certain conditions. Sharma and Deshpande [5] relaxed the conditions in [3] and proved the theorem. Later, Rashwan and Maustafa [4] claimed that the result in [5] is not valid, through an example. Nararaja Rao. I.H. et. al [2] claimed that the example does not qualify to be a counter example to the result in [5].

In this paper we show that the results of [3] and [5] are valid and thus put an end to the claims of [4] and [2]. Our proof is completely different from those of [3] and [5] and completeness of Menger space is not assumed.

AMS Mathematical subject classification (2010): 47H10, 54H25

Key words: Triangular norm, Menger space, compatible mappings.