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    Cone D-metric spaces with ?-distance and fixed point theorems of contractive mappings
    (Maltepe Üniversitesi, 2009) Lakzian, H.; Moghadan, E. Agheshte
    Naoki 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.
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    Weighted function algebra on weighted flows, compactifications of weighted flows, existence and none existence
    (Maltepe Üniversitesi, 2009) Lakzian, H.; Jahanpanah, R.
    During the past decade harmonic analysis on weighted semigroups has enjoyed considerable attention, and a good deal of results have been proved in this connection. H A M Dzinotyiweyi in 1984 first introduced the concept of weighted function algebra on groups and semigroups. Let S be a locally compact Hausdorff semitopological semigroup. A mapping wS : S ? (0, ?) is called a weight function on S if wS (st) ? wS (s)wS (t). Khadem-Maboudi A A and Pourabdollah M A in 1999 study the relationship between semigroups and weighted semigroups with the introduce means, homomorphisms, and compactifications of weighted semitopological semigroups. They also show that these compactifications do not retain all the nice properties of the ordinary semigroup compactifications unless we impose some restrictions on the weight functions. In this paper, we introduce a weight function on flow (S, X, ?) as follows: Let X is a locally compact Hausdorff topological space and a mapping wX : X ? (0, ?) is called a weight function on X if wX(sx) ? wX(s)wx(x). Then transform it to weighted flow ((S, wS ), (X, wX), ?). We define them corresponding to weighted flows compactifications. We also show that these compactifications do not retain all the nice properties of the ordinary flow compactifications unless we impose some restrictions on the weight functions.