Browsing by Author "Lakzian, Hossein"

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    Fixed Point Results on a Class of Generalized Metric Spaces
    (Springer Heidelberg, 2012) Aydi, Hassen; Karapinar, Erdal; Lakzian, Hossein; Mathematics
    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.