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Complete asymptotic expansions for the modified gamma operators
H. Karsli 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.4
The purpose of this paper is the study of the local rate of convergence of the modified Gamma operators (M_n,_kf) for functions in Wγ[0,∞). We investigate their asymptotic behaviour also for simultaneous approximation. As main results we derive the complete asymptotic expansions for modified Gamma operators.
Pointwise estimate for some Durrmeyer type operators
H. Karsli 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.2
In the present paper we investigate the behavior of some Durrmeyer type operators Ln(f; x), defined as Ln(f;x) = [수식] where the kernel Kn(x, t) may have different values. We give an estimate of the rate of pointwise convergence of these operators on a Lebesgue point of bounded variation function f defined on the interval [0, 1]. Using analysis techniques instead of probability methods we obtain the rate of pointwise convergence of the operators in question. Here we note that this kind of study is different from the earlier studies on such type of operators and have not been investigated for Durrmeyer type operators.
On convergence and rate of convergence of nonlinear singular integral operators
H. Karsli,E. Ibikli 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
Let G be a locally compact abelian group with the Haar measure. In the present paper we investigate both the pointwise convergence and the rate of convergence of the nonlinear integral operators, to a continuous and Lebesgue point of f 2 L1(a; b) as (x; ) ! (x0; 0).