Abstract
We solve the nonhomogeneous Legendre's differential equation and apply this result to obtaining a partial solution to the Hyers-Ulam stability problem for the Legendre's equation.
Highlights
Ulam gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems [1]
Among those was the question concerning the stability of homomorphisms
Let G1 be a group and let G2 be a metric group with a metric d(·, ·)
Summary
Alsina and Ger were the first authors who investigated the Hyers-Ulam stability of differential equations They proved in [8] that if a differentiable function f : I→R is a solution of the differential inequality |y (t) − y(t)| ≤ ε, where I is an open subinterval of R, there exists a solution f0 : I→R of the differential equation y (t) = y(t) such that | f (t) − f0(t)| ≤ 3ε for any t ∈ I.
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