Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Implicit Midpoint Procedures for Asymptotically Nonexpansive
  Mappings   The concept of asymptotically nonexpansive mappings is an important
generalization of the class of nonexpansive mappings. Implicit midpoint
procedures are extremely fundamental for solving equations involving nonlinear
operators. This paper studies the convergence analysis of the class of
asymptotically nonexpansive mappings by the implicit midpoint iterative
procedures. The necessary conditions for the convergence of the class of
asymptotically nonexpansive mappings are established, by using a well-known
iterative algorithm which plays important roles in the computation of fixed
points of nonlinear mappings. A numerical example is presented to illustrate
the convergence result. Under relaxed conditions on the parameters, some
algorithms and strong convergence results were derived to obtain some results
in the literature as corollaries.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin