Approximately linear recurrences

Abstract

In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.

Hyers–Ulam Stability of a Discrete Diamond-Alpha Derivative Equation

“…In this manner Ulam stability, also known as Hyers-Ulam stability or Hyers-Ulam-Rassias stability, has developed in the context of differential equations, difference equations (recurrences), functional equations, and operators; see Brillouët-Belluot, Brzdęk, and Ciepliński [4] for a survey of the literature on this topic, and also Brzdęk, Popa, Raşa, and Xu [5]. Honing in on Ulam stability in the discrete setting, see Popa [18,19], and more recently András and Mészáros [3] on time scales, Brzdęk and Wójcik [6], Hua, Li and Feng [12], Jung and Nam [14], Nam [15,16,17], Shen [22,23], and Rasouli, Abbaszadeh, and Eshaghi [20].…”

Ulam stability for nonautonomous quantum equations

“…Since Popa [39,40] began studying the Ulam stability of linear difference equations (linear recurrences) in 2005, many researchers have investigated this problem; for example, see [6,10,15,16,37,38,41,45]. For higher-order difference equations, see [13,14], and for nonlinear difference equations, see [26,[34][35][36].…”

Best Constant for Hyers–Ulam Stability of Second-Order h-Difference Equations with Constant Coefficients

“…In this way Ulam stability, also known as Hyers-Ulam stability or Hyers-Ulam-Rassias stability, has developed in the context of operators, functional equations, differential equations, and difference equations (recurrences); see Brillouët-Belluot, Brzdęk, and Ciepliński [6] for a good broad overview of the literature on this topic, or more recently Brzdęk, Popa, Raşa and Xu [7]. Particular to Ulam stability in the discrete setting, Popa [20,21] had some of the earlier papers, and more recently András and Mészáros [4], Brzdęk and Wójcik [8], Hua, Li and Feng [11], Jung and Nam [13], Nam [15,16,17], Shen [24], Rasouli, Abbaszadeh, and Eshaghi [22], and the present authors [1,2], have considered recurrences, difference equations, or dynamic equations on time scales in relation to Ulam stability, respectively.…”