Global smoothness preservation and the variation-diminishing property.
Grüss-type inequalities for positive linear operators with second order moduli
I-convergence theorems for a class of k-positive linear operators
In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.
Iterates of a class of discrete linear operators via contraction principle
In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.
Kantorovic Operators of Second Order.
Kantorovich-Stancu type operators.
King type modification of -Bernstein-Schurer operators
Very recently the -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve (2003), in this paper we modify -Bernstein-Schurer operators to King type modification of -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions and study the approximation properties of these operators. We establish a convergence theorem...
Korovkin Approximation in Waelbroeck Algebras.
Korovkin theory in Banach -algebras
Korovkin theory in liminal JB-algebras.
Korovkin Theory in Lindenstrauss Spaces.
Korovkin theory in normed algebras
If A is a normed power-associative complex algebra such that the selfadjoint part is normally ordered with respect to some order, then the Korovkin closure (see the introduction for definitions) of T ∪ {t* ∘ t| t ∈ T} contains J*(T) for any subset T of A. This can be applied to C*-algebras, minimal norm ideals on a Hilbert space, and to H*-algebras. For bounded H*-algebras and dual C*-algebras there is even equality. This answers a question posed in [1].
Korovkin-type convergence results for non-positive operators
Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. In this work we present qualitative Korovkin-type convergence results for a class of sequences of non-positive operators, more precisely regular operators with vanishing negative parts under a limiting process. Sequences of that type are called sequences of almost positive linear operators and have not been studied before in the context of Korovkin-type approximation theory. As an example...
Korovkin-type theorems and applications
Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.
Korovkin-type theorems for almost periodic measures
Some Korovkin-type theorems for spaces containing almost periodic measures are presented. We prove that some sets of almost periodic measures are test sets for some particular nets of positive linear operators on spaces containing almost periodic measures. We consider spaces which contain almost periodic measures defined by densities and measures which can be represented as the convolution between an arbitrary measure with finite support (or an arbitrary bounded measure) and a fixed almost periodic...
-approximation by iterative combination of Phillips operators.
approximation by multivariate Baskakov-Durrmeyer operator.
Lacunary equi-statistical convergence of positive linear operators
In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation...
Limit semigroups of Bernstein-Schnabl operators associated with positive projections
Limit semigroups of Stancu-Mühlbach operators associated with positive projections