**
D. Shulaia**

##
Solution of a Linear Integral Equation of Third Kind

**abstract:**

We study, in the class of Hölder functions, a nonhomogeneous linear integral
equation with coefficient cos x. Necessary and sufficient conditions for the
solvability of this equation are given under some assumptions on its kernel. The
solution is constructed analytically, using the Fredholm theory and the theory
of singular integral equations.