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In this paper we prove Korovkin type theorem for iterates of general positive linear operators T :C [0, 1] ! C [0, 1] and derive quantitative estimates in terms of modulus of smoothness. In particular...
Let T : X → X be a linear operator on a complex Banach space. Denote by (T ) and R(, T ) its spectrum and resolvent.
This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of Lp-fu...
In this paper we study the concept of S-linear operator and we show some of its properties and applications to the foundations of Quantum Mechanics. This new operators are a generalization of the li...
In this paper, we establish conditions under which a given well-defined linear operator that is not bounded on a given non-archimedean Hilbert space would be well-defined and bounded on another non-...
The notion of a probabilistic metric space was introduced by Menger in 1942. The notion of a probabilistic normed space was introduced in 1993. The aim of this paper is to give a necessary condition t...
We investigate certain positive linear operators Ln preserving the functions ek (x)=xk, k=0, 1, and modified operators Ln* which preserve e0 and e2. We show that the error of approximation of f by Ln*...
Let $T$ be a bounded linear operator in a Banach space, with $\sigma(T) = \{1\}$. In 1983, Esterle--Berkani' s conjecture was proposed for the decay of differences $\left ( I - T \right ) T\sp{n}$ as ...
In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and comp...
In the present paper, we introduce a sequence of linear operators, which is a higher order generalization of positive linear operators defined by a class of Borel measures studied in [2]. Then, using ...

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