Abstract
This paper is concerned to derive the main theorem of spectral relationships of Volterra-Fredholm integral equation (V-FIE) of the first kind in the space L-2[-1,1] x C[0,T], -1 <= x <= 1, 0 <= t <= T < 1. The Fredholm integral (FI) term is considered in position and its kernel takes a logarithmic form multiplying by a continuous function. While Volterra integral (VI) term in time with a positive continuous kernel. Many important special and new cases can be established from the main theorem. Moreover, we use it to solve V-FIE of the second kind in the same space. The numerical results are computed and the error is calculated using Maple 12. Copyright (C) 2010 John Wiley & Sons, Ltd.