The well-known result of Korovkin [4] states that for a sequence of positive linear operators [Kn]n 1 , such that Kn f converges uniformly to f in the particular cases f (t)=1, f (t)=t, and f (t)=t, then it also converges for every continuous real function f. The set [1, t, t] is called a Korovkin set. This result was a starting point for the development of a related theory. Since then many pap...

The present study introduces generalized ? -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence these types obtained for Lipschitz-type functions. Then, a Voronovskaja-type was given asymptotic behavior operators. Finally, numerical examples thei...

Abstract In this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified Gauss–Weierstrass, or Picard moment type operators. Pointwise convergence theorems are studied, using Korovkin-type theorem and Voronovskaja-type formula is obtained.

The origin of Korovkin Approximation theory is the classical theorem of P.P. Korovkin (1953),which says that for a sequence (Tn) of positive linear operators on C[a, b], in order to conclude the uniform convergence of Tnf to f for all f ∈ C[a, b], it suffices to check the uniform convergence only for the three functions f ∈ {1, x, x2}. Starting from this beautiful result many mathematicians hav...

We prove the basic fuzzy Korovkin theorem via a fuzzy Shisha– Mond inequality given here. This determines the degree of convergence with rates of a sequence of fuzzy positive linear operators to the fuzzy unit operator. The surprising fact is that only the real case Korovkin assumptions are enough for the validity of the fuzzy Korovkin theorem, along with a natural realization condition fulfill...

Here, in this article, we introduce and systematically investigate the ideas of deferred weighted statistical Riemann integrability summability for sequences functions. We begin by proving an inclusion theorem that establishes a relation between these two potentially useful concepts. also state prove Korovkin-type approximation theorems involving algebraic test functions using our proposed conc...

Here we start by proving the Riesz representation theorem for positive linear functionals on the space of continuous functions over a time scale. Then we prove further properties for the related Riemann–Stieltjes integral on time scales and we prove the related Hölder’s inequality. Next we prove the Hölder’s inequality for general positive linear functionals on time scales. We introduce basic c...