Abstract
In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.
Highlights
A famous question concerning the stability of homomorphisms was formulated by Ulam in 1940 [1]
We denote by L( f ) the Laplace transform of the function f, defined by
It is well known that the Laplace transform is linear and one-to-one if the involved functions are continuous
Summary
A famous question concerning the stability of homomorphisms was formulated by Ulam in 1940 [1]. In 1941 Hyers, [2] gave an answer, in the case of the additive Cauchy equation in Banach spaces, to the problem posed by Ulam [1]. Many mathematicians posed and solved similar problems by replacing functional equations with differential equations, partial differential equations or integral equations. The first result for Hyers–Ulam stability of differential equations was given by Obloza [3]. Alsina and Ger [4] investigated the stability of the differential equation y0 = y. In the papers [5,6,7,8,9,10], the stability of first-order linear differential equations and linear differential equations of higher order was studied
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