Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Suzuki-type fixed point theorem for nonlinear contractions   We introduce the notion of admissible functions and show that the family of
L-functions introduced by Lim in [Nonlinear Anal. 46(2001), 113--120] and the
family of test functions introduced by Geraghty in [Proc. Amer. Math. Soc.,
40(1973), 604--608] are admissible. Then we prove that if $\phi$ is an
admissible function, $(X,d)$ is a complete metric space, and $T$ is a mapping
on $X$ such that, for $\alpha(s)=\phi(s)/s$, the condition
$1/(1+\alpha(d(x,Tx))) d(x,Tx) < d(x,y)$ implies $d(Tx,Ty) < \phi(d(x,y))$, for
all $x,y\in X$, then $T$ has a unique fixed point. We also show that our fixed
point theorem characterizes the metric completeness of $X$.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci