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Let ((X,m)) be a complete M-metric space and (T: Xto X) be mapping satisfying the following condition: exists kinbiggl[0,frac{1}{2}biggr) quadtextit{such that}quad m(Tx,Ty leq kbigl(m x,Tx)+m y,Ty bigr) quadforall x,y in X. (6) Then T has a unique fixed point. The following definition is new version of the definition in [7] for an M-metric space.
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