Abstract

AbstractLet (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.KeywordsGeneralized metric spaceOperatorial equationUlam–Hyers stabilityUlam–Hyers–Rassias stabilityWeakly Picard operatorFixed point structureData dependence

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