Voronovskaya type asymptotic approximation by modified Gamma operators
Abstract In this paper we deal with the following modified Gamma operators A n ( f ; x ) = ∫ 0 ∞ K n ( x , t ) f ( t ) dt , defined for any f for which the last integral is convergent, where K n ( x , t ) = ( 2 n + 3 ) ! n ! ( n + 2 ) ! · t n · x n + 3 ( x + t ) 2 n + 4 , x , t ∈ ( 0 , ∞ ) . We study some direct results in asymptotic approximation.
Approximation by certain linear operators preserving x^2
We investigate certain positive linear operators Ln preserving the functions ek(x) = x k , k = 0, 1, and modified operators Ln which preserve e0 and e2 . We show that the error of approximation of f by L ∗ n(f) is smaller than for Ln(f) .
Beyond East–West: Marginality and National Dignity in Finnish Identity Construction
Since the end of the Cold War it has become common for Finnish academics and politicians alike to frame debates about Finnish national identity in terms of locating Finland somewhere along a continuum between East and West. Indeed, for politicians, properly locating oneself (and therefore Finland) along this continuum has often been seen as central to the winning and losing of elections. For example, the 1994 referendum on EU membership was largely interpreted precisely as an opportunity to relocate Finland further to the West. Indeed, the tendency to depict Finnish history in terms of a series of “Westernizing” moves has been notable, but has also betrayed some of the politicized elements of this view. However, this framing of Finnish national identity discourse is not only sometimes politicized but arguably is also too simplified and results in blindness towards other identity narratives that have also been important through Finnish history, and that are also evident (but rarely recognized) today as well. In this article we aim to highlight one of these that we argue has played a key role in locating Finland in the world and in formulating notions of what Finland is about, what historical role and mission it has been understood as destined to play, and what futures for the nation have been conceptualized as possible and as providing a source of subjectivity and national dignity.