We investigate Hyers-Ulam stability of the first order difference equation x i+1 = ax i +b cx i +d , where ad − bc = 1, c = 0 and |a + d| > 2. It has Hyers-Ulam stability if the initial point x 0 lies in some definite interval of R. The condition |a + d| > 2 implies that the above recurrence is a natural generalization of Pielou logistic difference equation.
We prove Hyers-Ulam stability of the first-order difference equation of the form +1 = ( , ), where is a given function with some moderate features. Moreover, we introduce some conditions for the function under which the difference equation is not stable in the sense of Hyers and Ulam.
If a differentiable function f : [a, b] → R and a point η ∈ [a, b] satisfy f (η) − f (a) = f (η)(η − a), then the point η is called a Flett's mean value point of f in [a, b]. The concept of Flett's mean value points can be generalized to the 2-dimensional Flett's mean value points as follows: For the different pointsr andŝ of R × R, let L be the line segment joiningr andŝ. If a partially differentiable function f : R × R → R and an intermediate pointω ∈ L satisfy f (ω) − f (r) = ω −r, f (ω) , then the pointω is called a 2-dimensional Flett's mean value point of f in L. In this paper, we will prove the Hyers-Ulam stability of 2-dimensional Flett's mean value points.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.