Abstract：In this paper, we first introduce the notion of D*-metric space and the related knowledge. Based on the D*-metric space, we extend the generalized weakly contractive maps related to two kinds of distance control functions (ψ,?) from metric space to the D*-metric space,and discuss the existence and uniqueness of fixed point under generalized weakly contractive conditions by constructing iterative sequences.We also present several new fixed point theorems. The results enrich the fixed point theory of D*-metric space.
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