Abstract Korovkin-type theorems via nonlinear operators in modular function spaces with power series methods

Abstract

In this paper, we present new abstract versions of Korovkin-type approximation theorems in the framework of modular spaces by employing sequences of monotone and sublinear operators with respect to power series methods. We further calculate the rate of convergence in terms of modulus of continuity and demonstrate the applicability of our abstract results through Bernstein–Kantorovich and Bernstein–Kantorovich–Choquet operators in Orlicz spaces under non-additive measures. Finally, we relax the monotonicity of the sublinear operators in the modular Korovkin theorem.