Stability of the Banach space valued Chebyshev differential equation

Abstract We prove that, if f is an approximate solution of the Banach space valued Chebyshev differential equation ( 1 − x 2 ) y ″ ( x ) − x y ′ ( x ) + n 2 y ( x ) = 0 for x ∈ ( − 1 , 1 ) , then f is near to an exact solution.