Approximation of Abstract Korovkin-Type via Monotone Sublinear Operators: A Power Series Methods and Modified Operators

This paper introduces a novel framework for approximation through monotone and sublinear operators using the power series method to unify and extend abstract Korovkin-type results. We establish abstract Korovkin-type approximation theorems that are applicable across both a locally compact metric space (as well as a compact metric space) and a compact Hausdorff space. Our results extend previous works by establishing approximation results for nonlinear operators in different function spaces under regular summability methods. We also use a modified modulus of continuity, adapted to the structural properties of the space under consideration, which allows us to derive quantitative estimates. Furthermore, we illustrate the theoretical findings through constructed examples of monotone sublinear operators, including several multivariate extensions developed and analyzed here for the first time.