An Abstract Version of the Korovkin Theorem via $${\mathcal{A}}$$ A -summation process

Abstract Korovkin type theorems on modular spaces by $\mathscr{A}$-summability

“…Our aim is to change classical test functions of Korovkin theorem on modular spaces by using A -summability. Similar problems have been studied in [1], [2], [3], [4].…”

Korovkin-type approximation by operators in Riesz spaces via power series method

“…A few years later in [5], Guessab and Schmeisser generalized the classical Korovkin theorem for positive linear operators on C(Ω) spaces. Later in [6], Atlihan and Taş proved a Korovkin-type Approximation theorem with respect to A-summation processes. A Banach lattice version of Korovkin's theorem has been established and is due to Wiśniewska and Wójtowicz (see [7]).…”

Abstract Korovkin Theory in Modular Spaces in The Sense of Power Series Method

“…There are also trigonometric versions of this theorem with the test functions {1, cos x, sin x} and abstract Korovkin type results have also been studied [14,18]. Later on Korovkin type theorems have been extended in various directions with dierent aims such as nding other subsets satisfying the same property {1, x, x 2 }, establishing the same results in other function spaces, abstract Banach spaces [1,2,3]. Recently some versions of Korovkin type theorems have been proved in modular spaces which include as particular cases L p , Orlicz and Musielak-Orlicz spaces [9,21].…”