<p>The article derives exact solutions of nonlinear equations with multi-kernel general fractional derivatives and integrals, and periodic kicks. To derive these solutions, the fundamental theorems of the multi-kernel general fractional calculus (GFC) are used. Then, using these solutions, we obtain multi-kernel general discrete maps with general form of memory functions that are represented by the Sonin kernels that describe non-locality in time. For the first time, discrete maps were obtained from fractional differential equations in 2008. This paper generalizes this approach to obtaining discrete maps with memory and non-locality in time from fractional derivatives and integrals to operators of the multi-kernel GFC. The importance of this approach is based on the exact connection (without any approximations) between nonlinear fractional differential and integral equations and nonlinear discrete maps with memory. The proposed multi-kernel general discrete maps are generalization of the well-known universal map, the Anosov map, the logistic map, standard or Chirikov-Taylor map without memory and with power-law type memory. Examples of the application of these maps with memory in social and economic models are proposed in the article.</p>