Lakzian, H.Moghadan, E. Agheshte2024-07-122024-07-122009Lakzian, H. ve Moghadan, E. A. (2009). Cone D-metric spaces with ?-distance and fixed point theorems of contractive mappings. Maltepe Üniversitesi, s. 175.9.78605E+12https://hdl.handle.net/20.500.12415/2223Naoki Shioji, Tomonari Suzuki and Wataru Takahashi in 1995 describe the relationship between weakly contractive mappings and weakly Kannan mappings. They discuss characterizations of metric completeness which are connected with the existence of fixed points for mappings and then they showed that a metric space is complete if it has the fixed point property for Kannan mappings. Huang Long-Guang, Zhang Xian in 2007 introduced cone metric space and then they proved some fixed point theorems of contractive mappings on cone metric spaces. Recently, Dhage in 1992 introduced the concept of D-metric. Afterwards Y.J.Cho and R.Saadati in 2006 introduced a ?-distance on a D-metric space which is a generalization of the concept of w-distance due to Kada, Suzuki and Takahashi in 1995. This generalization is non trivial because a D-metric doesn’t always define a topology, and even when it does, this topology is not necessarily Hausdorff . In this paper, we first introduce cone D-metric spaces with ?-distance. Then we describe the relationship between weakly contractive mappings and weakly Kannan mappings on this spaces. We discuss characterizations of cone D-metric spaces with ?-distance completeness which are connected with the existence of fixed points for mappings and then we show that a cone D-metric spaces with ?-distance is complete if it has the fixed point property for Kannan mappings.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessConference Object176175