On the theory of convolution equations of the third kind, II

Existence results of Part I of the paper are generalized to two types of autoconvolution equations of the third kind having free terms with nonzero values at x = 0 like the well-known Bernstein–Doetsch equation for the Jacobian theta zero functions. Also uniqueness results for the linear convolution equations in Part I of the paper are extended to more general function spaces. Further, a special class of integro-differential equations with autoconvolution integral and two classes of the linear singular Abel–Volterra equations are dealt with. © 2007 Elsevier Inc. All rights reserved.