Geodesic
CONTRACTIONS OVER GENERALIZED METRIC SPACES
SARMA, I. R.1 ; RAO2, J. M.2 ; RAO, S. S.3
1 FED-II, K.L. University, Vaddeswaram-522502, Guntur district, Andhra Pradesh, India
2 Principal, Vijaya Engineering College, Wrya Road, Khammam-507305, Andhra Pradesh, India
3 Department of Basics Sciences and Humanities, Joginpally B.R. Engineering College, Yenkapally(V), Moinabad(M), Ranga Reddy Distric, Andhra Pradesh- 500075, India.
Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 3, p. 180-182.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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 [1] 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.
DOI : 10.22436/jnsa.002.03.06
Classification : 47H10, 54H25
Keywords: Fixed point, Contraction mapping, Generalized metric spaces

SARMA, I. R. 1 ; RAO2, J. M. 2 ; RAO, S. S. 3

1 FED-II, K.L. University, Vaddeswaram-522502, Guntur district, Andhra Pradesh, India
2 Principal, Vijaya Engineering College, Wrya Road, Khammam-507305, Andhra Pradesh, India
3 Department of Basics Sciences and Humanities, Joginpally B.R. Engineering College, Yenkapally(V), Moinabad(M), Ranga Reddy Distric, Andhra Pradesh- 500075, India. 
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SARMA, I. R.; RAO2, J. M.; RAO, S. S. CONTRACTIONS OVER GENERALIZED METRIC SPACES. Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 3, p. 180-182. doi : 10.22436/jnsa.002.03.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.002.03.06/

[1] Branciari, A. A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Publ. Math. Debrecen, Volume 57 (2000), pp. 31-37

[2] Azam, A.; Arshad, M. Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl., Volume 1 (2008), pp. 45-48

[3] Akram, M.; Siddiqui, Akhlaq A. A fixed point theorem for A-Contractions on a class of generalized metric spaces, Korean J. Math. Sciences., Volume 10 (2003), pp. 1-5

[4] Lahiri, B. K.; Das, P. tFixed point of a Ljubomir Ciric’s quasi-contraction mapping in a generalized metric spaces, Publ. Math. Debrecen, Volume 61 (2002), pp. 584-594

[5] Das, Pratulananda; Dey, L. K. A fixed point theorem in a Generalized metric space, Soochow Journal of Mathematics, Volume 33 (2007), pp. 33-39

[6] Das, P. A. A fixed point theorem on a class of Generalized metric spaces, Korean J.Math.Scienes, Volume 9 (2002), pp. 29-33

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