Stability of functional equations in single variable

By Ravi P. Agarwal, Bing Xu, Weinian Zhang. 2003

168 citations recorded by the source corpus.

Abstract This paper discusses Hyers–Ulam stability for functional equations in single variable, including the forms of linear functional equation, nonlinear functional equation and iterative equation. Surveying many known and related results, we clarify the relations between Hyers–Ulam stability and other senses of stability such as iterative stability, continuous dependence and robust stability, which are used for functional equations. Applying results of nonlinear functional equations we give the Hyers–Ulam stability of Bottcher's equation. We also prove a general result of Hyers–Ulam stability for iterative equations.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/052b2ed23e1ef508e028c12c566656808787ff0f

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In Applied Mathematics

Citations in the corpus

Applications of fixed point theorems to the Hyers-Ulam stability of functional equations–a survey (2012, background): “After his result a great number of papers (see for instance monographs [23, 26, 29], survey articles [1, 18, 24, 39, 40, 43] and the references given there) on the subject have been published, generalizing Ulam’s problem and Hyers’s theorem in various directions and to other equations (as the words ”
Approximately generalized additive functions in several variables (2010, methodology): “Approximately additive functions by using alternative fixed point Baker [7] was the first author who applied the fixed point method in the study of Hyers–Ulam stability (see also [2]).”
Fixed Point Theory and the Ulam Stability (2014, background): “After his result a great number of papers (see for instance monographs [3–5], survey articles [6–14], and the references given there) on the subject have been published, generalizing Ulam’s problem and Hyers’s theorem in various directions and to other (not necessarily functional) equations.”
Hyers-Ulam-Rassias stability of a linear recurrence (2005, background): “As is mentioned in [1] there are much less results on stability for functional equations in a single variable than in several variables.”
Note on nonstability of the linear recurrence (2006, background): “[ 1 , 9]) of the original problem, raised by S. M. ULAM in 1940, we introduce the following two definitions (cf.”
On Ulam’s Type Stability of the Linear Equation and Related Issues (2014, methodology): “Below, we present some outcomes obtained by Turdza in [62], which have not been included in [7].”