期刊论文详细信息
Proceedings Mathematical Sciences
Positive Linear Operators Generated by Analytic Functions
Sofiya Ostrovska1 
[1] Department of Mathematics, Atilim University, 0 Incek, Ankara, Turkey$$
关键词: Szász–Mirakyan operator;    positive operator;    limit 𝑞-Bernstein operator;    𝑞-integers;    Poisson distribution;    totally positive sequence.;   
DOI  :  
学科分类:数学(综合)
来源: Indian Academy of Sciences
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【 摘 要 】

Let 𝜑 be a power series with positive Taylor coefficients ${a_k}^∞_{k=0}$ and non-zero radius of convergence 𝑟 ≤ ∞. Let $𝜉_x,,0≤ x < r$ be a random variable whose values $𝛼_k, k=0,1,ldots,$ are independent of 𝑥 and taken with probabilities $a_kx^k/varphi(x), k=0,1,ldots$The positive linear operator $(A_varphi f)(x):=E[f(𝜉_x)]$ is studied. It is proved that if $E(𝜉_x)=x,E(𝜉^2_x)=qx^2+bx+c,, q, b, cin R, q>0$, then $A_varphi$ reduces to the Szász–Mirakyan operator in the case 𝑞=1, to the limit 𝑞-Bernstein operator in the case 0 < 𝑞 < 1, and to a modification of the Lupaş operator in the case 𝑞>1.

【 授权许可】

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