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Interval methods for fixed-point problems [PDF]

Numerical Functional Analysis and Optimization, 1987
Interval analysis is applied to the fixed-point problem x=ϕ(x) for continuous ϕ:S→S, where the space S is constructed from Cartesian products of the set R of real numbers, with componentwise definitions of arithmetic operations, ordering, and the product topology. With the aid of an interval inclusion φ:IS → IS in the interval space IS corresponding to
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On the Fixed Point Method and Bloch’s Theorem

Michigan Mathematical Journal, 2021
In this paper, via the contraction mapping principle, we give a proof of a Bloch-type theorem for normalized harmonic Bochner–Takahashi K-mappings and for solutions to equations of the form Pu=0, where P is a homogeneous differential operator with an analytic fundamental solution, that is, homogeneous elliptic operators with constant coefficients.
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An improvement to the fixed point iterative method

Applied Mathematics and Computation, 2006
The problem of convergence of the fixed point iterative method has been studied in this article. The main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations. A technique is presented to increase the order of convergence as much as desired.
Jafar Biazar, Alireza Amirteimoori
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The fixed point method in analysis.

1936
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The sandwich method for computing fixed points

ACM SIGMAP Bulletin, 1973
Many equilibrium and optimization problems in economics and operations research can be put in the form: Find x such that f(x) = x, where x is a nonnegative vector with component sum one and f is a continuous function (not necessarily differentiable, convex, or concave).
H. W. Kuhn, J. G. MacKinnon
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Extensions of the Fix-Point Method I: The GEID estimata and the fractional Fix-Point Method

Économie appliquée, 1973
Ågren Anders. Extensions of the Fix-Point Method I: The GEID estimata and the fractional Fix-Point Method. In: Économie appliquée, tome 26 n°2-4,1973. pp. 561-582.
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Iterative methods for interval inclusion of fixed points

BIT, 1978
The paper discusses a technique for handling numerical, iterative processes that combines the efficiency of ordinary floating-point iterations with the accuracy control that may be obtained by iterations in interval arithmetic. As illustration the technique is used for the solution of fixed point problems in one and several variables.
Ole Caprani, Kaj Madsen
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A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems

Journal of Optimization Theory and Applications, 2023
Xuezhong Wang, Ping Wei, Yimin Wei
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Corrigendum: On analytic model for two-choice behavior of the paradise fish based on the fixed point method, J. Fixed Point Theory Appl. 2019, 21:56

Journal of Fixed Point Theory and Applications, 2020
A. Turab, W. Sintunavarat
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A fixed point multiple shooting method

Computing, 1988
A method is proposed for solving ordinary two-point boundary value problems of a certain type. It works if the problem can be transformed into a contracting fixed point equation by means of a Green's function which need not be known for the process. It is similar to multiple shooting but much simpler.
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