Fixed point results on a class of generalized metric spaces

Abstract

Brianciari (‘A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,’ Publ. Math. Debrecen 57 (2000) 31-37) initiated the notion of the generalized metric space as a generalization of a metric space in such a way that the triangle inequality is replaced by the ‘quadrilateral inequality,’ d(x,y) ≤ d(x,a) + d(a,b) + d(b,y) for all pairwise distinct points x,y,a, and b of X. In this paper, we establish a fixed point result for weak contractive mappings T : X → X in complete Hausdorff generalized metric spaces. The obtained result is an extension and a generalization of many existing results in the literature.