Fixed Point Theorem in Sequence of Hausdorff Left (Right) Sequentially Complete Quasi-Gauge Spaces

P. V. Subrahmanyam in the paper [7] has exploited the technique of Banach’s contraction principle in proving the fixed point theorem in Hausdorff left (right) sequentially complete quasi-gauge spaces. He has not only generelised the results of Chatterjea [1], Kannan [2,3], Reilly[4,5] and Singh[6], but unified their results by takeing the quasi-gauge spaces due to Reilly [4]. All these authors have only proved the fixed point theorem for a single complete metric space. In this paper I have followed the above technique in proving the fixed point for sequence of Hausdorff left (right) sequentially complete quasi-gauge spaces, by defining their Cartesian product as a set X = _i^X_i of sequences where x_(n ) 〖∈X〗_n given by the quasi-pseudo –metric p(x,y) =∑_1^ ∞(〖p_(n ) (x_(n,) y〗_(n )))/(n![1+p_(n))]) 〖x_(n ),y〗_(n ) )])