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Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Antonio Attalienti, Ioan Rasa (2008)

Czechoslovak Mathematical Journal

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...

Shift invariant operators and a saturation theorem

Karol Dziedziul (2003)

Applicationes Mathematicae

The properties of shift invariant operators Q h are proved: It is shown that Q has polynomial order r iff r is the rate of convergence of Q h . A weak saturation theorem is given. If f is replaced by Q f h in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.

Some Applications of new Modified q-Szász–Mirakyan Operators

Ramesh P. PATHAK, Shiv Kumar SAHOO (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper we introducing a new sequence of positive q-integral new Modified q-Szász-Mirakyan Operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on [ 0 , ∞ ) . Weighted statistical approximation theorem, Korovkin-type theorems for fuzzy continuous functions, an estimate for the rate of convergence and some properties are also obtained for these operators.

Statistical approximation properties of q-Baskakov-Kantorovich operators

Vijay Gupta, Cristina Radu (2009)

Open Mathematics

In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.

Strong unicity criterion in some space of operators

Grzegorz Lewicki (1993)

Commentationes Mathematicae Universitatis Carolinae

Let X be a finite dimensional Banach space and let Y ⊂ X be a hyperplane. Let L Y = { L ∈ L ( X , Y ) : L ∣ Y = 0 } . In this note, we present sufficient and necessary conditions on L 0 ∈ L Y being a strongly unique best approximation for given L ∈ L ( X ) . Next we apply this characterization to the case of X = l ∞ n and to generalization of Theorem I.1.3 from [12] (see also [13]).

Symmetric subspaces of l 1 with large projection constants

Bruce Chalmers, Grzegorz Lewicki (1999)

Studia Mathematica

We construct k-dimensional (k ≥ 3) subspaces V k of l 1 , with a very simple structure and with projection constant satisfying λ ( V k ) ≥ λ ( V k , l 1 ) > λ ( l 2 ( k ) ) .

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