In this paper we show that the function , () p fLI α ∈ ,0<p<1 where I=[-1,1] can be approximated by an algebraic polynomial with an error not exceeding , 1 ( , , ) kp ft n ϕ αω where
,
1 ( , , ) kp ft n ϕ αω is the Ditizian–Totik modules of smoothness of unbounded function in , () p LI
In this paper, two parameters for the Exponential distribution were estimated using the
Bayesian estimation method under three different loss functions: the Squared error loss function,
the Precautionary loss function, and the Entropy loss function. The Exponential distribution prior
and Gamma distribution have been assumed as the priors of the scale γ and location δ parameters
respectively. In Bayesian estimation, Maximum likelihood estimators have been used as the initial
estimators, and the Tierney-Kadane approximation has been used effectively. Based on the MonteCarlo
simulation method, those estimators were compared depending on the mean squared errors (MSEs).The results showed that the Bayesian esti
Convergence prop erties of Jackson polynomials have been considered by Zugmund
[1,ch.X] in (1959) and J.Szbados [2], (p =ï‚¥) while in (1983) V.A.Popov and J.Szabados [3]
(1 ï‚£p ï‚£ ï‚¥) have proved a direct inequality for Jackson polynomials in L
p-sp ace of 2ï°-periodic bounded Riemann integrable functions (f R) in terms of some modulus of
continuity .
In 1991 S.K.Jassim proved direct and inverse inequality for Jackson polynomials in
locally global norms (L
ï¤,p) of 2ï°-p eriodic bounded measurable functions (f Lï‚¥) in terms of
suitable Peetre K-functional [4].
Now the aim of our paper is to proved direct and inverse inequalities for Jackson
polynomials
ÖZET
Irak’ın osmanlıcada yazılan sayısız elyazmalar çeşitli illerinde bulunur. Bunlardan Irak’ın başkenti olan Bağdat’tır. Irak Ulusal Müzesi Bağdad’ın uygarlık yerlerindendir. Elyazması Evi müzenin en önemli bölümleri sayılır. Orada osmanlıcada yazılan çok değerli elyazmalar bulunur. Bu elyazmalarından birisini ( fotokopi ) elde edip üzerinde çalışılmaktadır. Eser Antoloji şeklinde yazılmış. Bu eserden Sadullah Pâşâ’nın On Dokuzuncu Asır Manzumesini seçip ele alınmaktadır.
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