Fixed point theorems of Ciric-Matkowski type in generalized metric spaces

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A self-map T of a ν-generalized metric space (X,d) is said to be a Ciric-Matkowski contraction if d(Tx,Ty)<d(x,y), for x≠ y, and, for every ε>0, there is δ>0 such that d(x,y)<δ+ε implies d(Tx,Ty)≤ ε. In this paper, fixed point theorems for this kind of contractions of ν-generalized metric spaces, are presented. Then, by replacing the distance function d(x,y) with functions of the form m(x,y)=d(x,y)+γ(d(x,Tx)+d(y,Ty)), where γ>0, results analogue to those due to P.D. Proiniv (Fixed point theorems in metric spaces, Nonlinear Anal. 46 (2006) 546--557) are obtained.