I. R. SARMA - FED-II, K.L. University, Vaddeswaram-522502, Guntur district, Andhra Pradesh, India. J. M. RAO2 - Principal, Vijaya Engineering College, Wrya Road, Khammam-507305, Andhra Pradesh, India. S. S. RAO - Department of Basics Sciences and Humanities, Joginpally B.R. Engineering College, Yenkapally(V), Moinabad(M), Ranga Reddy Distric, Andhra Pradesh- 500075, India..
A generalized metric space (g.m.s) has been defined as a metric space in which the triangle inequality is replaced by the ‘Quadrilateral inequality’, \(d(x, y) \leq d(x, a) + d(a, b) + d(b, y)\) for all pairwise distinct points \(x, y, a\) and \(b\) of \(X. (X, d)\) becomes a topological space when we define a subset \(A\) of \(X\) to be open if to each a in \(A\) there corresponds a positive number \(r_a\) such that \(b \in A\) whenever \(d(a, b) < r_a\). Cauchyness and convergence of sequences are defined exactly as in metric spaces and a g.m.s \((X, d)\) is called complete if every Cauchy sequence in \((X, d)\) converges to a point of \(X\). A.Branciari  has published a paper purporting to generalize Banach’s Contraction principle in metric spaces to g.m.s. In this paper we present a correct version and proof of the generalization.
I. R. SARMA, J. M. RAO2, S. S. RAO, CONTRACTIONS OVER GENERALIZED METRIC SPACES, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 3, 180-182
SARMA I. R., RAO2 J. M., RAO S. S., CONTRACTIONS OVER GENERALIZED METRIC SPACES. J. Nonlinear Sci. Appl. (2009); 2(3):180-182
SARMA, I. R., RAO2, J. M., RAO, S. S.. " CONTRACTIONS OVER GENERALIZED METRIC SPACES." Journal of Nonlinear Sciences and Applications, 2, no. 3 (2009): 180-182