Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fixed point theorem for contractions in modular metric spaces   The notion of a (metric) modular on an arbitrary set and the corresponding
modular space, more general than a metric space, were introduced and studied
recently by the author [V. V. Chistyakov, Metric modulars and their
application, Dokl. Math. 73(1) (2006) 32-35, and Modular metric spaces, I:
Basic concepts, Nonlinear Anal. 72(1) (2010) 1-14]. In this paper we establish
a fixed point theorem for contractive maps in modular spaces. It is related to
contracting rather ``generalized average velocities'' than metric distances,
and the successive approximations of fixed points converge to the fixed points
in a weaker sense as compared to the metric convergence.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga