A solution of the problem of inverse approximation for the sampling Kantorovich operators in case of Lipschitz functions

The study of inverse results of approximation for the family of sampling Kantorovich operators in case of alpha-Holder function, 0 < alpha < 1, has been solved in a recent paper of some of the authors. However, the limit case of Lipschitz functions, i.e., when alpha = 1, in which standard methods fail, remained unsolved. In this paper, a solution of the above open problem of inverse approximation has been proposed