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...
Kriterien erster und zweiter Ordnung für lokal beste Approximationen bei Problemen mit Nebenbedingungen. - On First and Second Order Conditions for Locally Best Approximations for Constraint Problems.
Kriterien zweiter Ordnung für lokal beste Approximationen.
Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation.
Krovkin Systems of Stochastic Processes.
Kubaturformeln mit minimaler Knotenzahl. -Minimum-Point Cubature Formulas.
spaces fail a certain approximative property.
expansions in series of fractional parts.
-approximation by iterative combination of Phillips operators.
approximation by multivariate Baskakov-Durrmeyer operator.
-approximation by the method of integral Meyer-König and Zeller operators
-approximation of generalized biaxially symmetric potentials over Carathéodory domains
-convergence of Bernstein-Kantorovich-type operators
We study a Kantorovich-type modification of the operators introduced in [1] and we characterize their convergence in the -norm. We also furnish a quantitative estimate of the convergence.
inequalities for the growth of polynomials with restricted zeros
Let be a polynomial of degree at most which does not vanish in the disk , then for and , Boas and Rahman proved In this paper, we improve the above inequality for by involving some of the coefficients of the polynomial . Analogous result for the class of polynomials having no zero in is also given.
inequalities for the polar derivative of a polynomial.