%0 Journal Article %T Suzuki-type fixed point theorems for generalized contractive mappings‎ ‎that characterize metric completeness %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Abtahi, M. %D 2015 %\ 08/01/2015 %V 41 %N 4 %P 931-943 %! Suzuki-type fixed point theorems for generalized contractive mappings‎ ‎that characterize metric completeness %K Banach contraction principle %K Contractive mappings %K Fixed points %K Suzuki-type fixed point theorem %K Metric completeness %R %X ‎Inspired by the work of Suzuki in‎ ‎[T. Suzuki‎, ‎A generalized Banach contraction principle that characterizes metric completeness‎, Proc‎. ‎Amer‎. ‎Math‎. ‎Soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of Geraghty in [M.A‎. ‎Geraghty‎, ‎On contractive mappings‎, ‎Proc‎. ‎Amer‎. ‎Math‎. ‎Soc., ‎40 (1973)‎, ‎604--608]‎and characterizes metric completeness‎. ‎We introduce the family $A$ of all nonnegative functions‎ ‎$\phi$ with the property that‎, ‎given a metric space $(X,d\,)$ and a mapping $T:X\to X$‎, ‎the condition‎ ‎\[‎ ‎x,y\in X,\ x\neq y,\ d(x,Tx) \leq d(x,y)\ \Longrightarrow\‎ ‎d(Tx,Ty) < \phi(d(x,y))‎, ‎\]‎ ‎implies that the iterations $x_n=T^nx$‎, ‎for any choice of initial point $x\in X$‎, ‎form a Cauchy sequence in $X$‎. ‎We show that the family of L-functions‎, ‎introduced by Lim in [T.C‎. ‎Lim‎, ‎On characterizations of Meir-Keeler contractive maps‎, Nonlinear Anal.‎, 46 (2001)‎, ‎113--120]‎, ‎and the family‎ ‎of test functions‎, ‎introduced by Geraghty‎, ‎belong to $A$‎. ‎We also prove‎ ‎a Suzuki-type fixed point theorem for nonlinear contractions‎. %U http://bims.iranjournals.ir/article_663_0604fdcf93c19e80e22d9c7c6f7e3b03.pdf