Uniform convergence of a sequence of functions at a point

Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory

“…The idea of uniform convergence of a sequence of functions at a point was defined by J. Klippert and G. Williams in [18]. This type of convergence is a stronger method than the well known uniform convergence.…”

“…Recently, Demirci et al [19] gave the notion of relative uniform convergence of a sequence of functions at a point and they proved the Korovkin type approximation theorems. Now we recall these interesting types of convergences: Definition 2.1 [18] Suppose that ( ) is a sequence of real functions defined on ⊂ ℝ. Let 0 ∈ .…”

“…Another interesting type of convergence is the uniform convergence of a sequence of functions at a point [18]. More recently, Demirci et al [19] extended this type of convergence to relative uniform convergence of a sequence of functions at a point where the set of the neighborhoods of the point at which relative uniform convergence is considered (see, e.g., [20,21]).…”

Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

“…In [28] some Korovkin-type theorems are proved in the setting of relative uniform convergence with respect to scale functions, investigated in [20][21][22]37], and different examples and applications are given.…”