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 ð‘ž-Bernstein operator; ð‘ž-integers; Poisson distribution; totally positive sequence.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
Let 𜑠be a power series with positive Taylor coefficients ${a_k}^∞_{k=0}$ and non-zero radius of convergence 𑟠≤ ∞. Let $ðœ‰_x,,0≤ x < r$ be a random variable whose values $ð›¼_k, k=0,1,ldots,$ are independent of ð‘¥ and taken with probabilities $a_kx^k/varphi(x), k=0,1,ldots$The positive linear operator $(A_varphi f)(x):=E[f(ðœ‰_x)]$ is studied. It is proved that if $E(ðœ‰_x)=x,E(ðœ‰^2_x)=qx^2+bx+c,, q, b, cin R, q>0$, then $A_varphi$ reduces to the Szász–Mirakyan operator in the case ð‘ž=1, to the limit ð‘ž-Bernstein operator in the case 0 < ð‘ž < 1, and to a modification of the LupaÅŸ operator in the case ð‘ž>1.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912040506797ZK.pdf | 118KB | download |