Sequences of maps and convergence properties of first-order difference equations with variable coefficients

We consider sequences of continuous functions on that converge to a continuous monotone limit function. We prove a convergence theorem for the iterative map This result is used to solve an open problem in the field concerning the convergence properties of first-order rational difference equations th...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 23; no. 4; pp. 779 - 798
Main Authors Huang, Ying Sue, Knopf, Peter M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.04.2017
Taylor & Francis Ltd
Subjects
Continuity (mathematics)
Convergence
Difference equations
Iterative methods
Mathematical analysis
Nonlinear programming
Properties (attributes)
Sequences
variable coefficients
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ISSN1023-6198
1563-5120
DOI10.1080/10236198.2017.1282952

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Summary:We consider sequences of continuous functions on that converge to a continuous monotone limit function. We prove a convergence theorem for the iterative map This result is used to solve an open problem in the field concerning the convergence properties of first-order rational difference equations that are linear in numerator and denominator with variable coefficients. We also establish convergence properties for a certain class of systems of first-order difference equations.
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ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2017.1282952