Ulam Stability of the Operatorial Equations

Ioan A. Rus ()
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Ioan A. Rus: Babeş–Bolyai University

Chapter Chapter 23 in Functional Equations in Mathematical Analysis, 2011, pp 287-305 from Springer

Abstract: Abstract Let (E, +, ℝ, ≤, → ) be an ordered linear L-space, $${E}_{+} :=\{ e \in E\ \vert \ e \geq 0\}$$ , (X, d) and (Y, ρ) be two generalized metric spaces with d(x, y), ρ(x, y) ∈ E +, and f, g : X → Y be two operators. In this paper we present for the coincidence equation $$f(x) = g(x)$$ four types of Ulam stability: Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability. Some illustrative examples are given, the relations of Ulam stability with the weakly Picard operator are studied and two research directions are also presented.

Keywords: Generalized metric space; Operatorial equation; Ulam–Hyers stability; Ulam–Hyers–Rassias stability; Weakly Picard operator; Fixed point structure; Data dependence (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_23

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DOI: 10.1007/978-1-4614-0055-4_23

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