On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces Original Research Article

A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for s∈G, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.