On the Uniform Convergence of Fourier Series Expansions for Sturm-Liouville Problems with a Spectral Parameter in the Boundary Conditions

In this paper, we study the uniform convergence of the spectral expansions in terms of eigenfunctions of the boundary value problem -y '' q (x) y = lambda y, 0 < x < 1, (a(0)lambda + b(0)) y (0) = (c(0)lambda + d(0)) y' (0), (a(1)lambda + b(1)) y (1) = (c(1)lambda + d(1)) y' (1) where lambda is a spectral parameter, q (x) is a real-valued continuous function on the interval [0, 1] and a(k), b(k), c(k), d(k) (k = 0,1) are real constants which satisfy the conditions sigma(k) = (-1)(k) (a(k)d(k) - b(k)c(k)) < 0 (k = 0, 1).