由某些特殊函數所建構的正線性算子暨一些差分方程之研究

Certain Positive Linear Operators Constructed by Some Special Functions and Some Difference Equations

蔡育典(Yu-Dian Tasi)

指導教授 ： 陳功宇

淡江大學/理學院/數學學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00233

摘要

我們主要是研究下列型態的差分方程式有界解和無界解的存在性及行為。
a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2-S^2}
，其中{c_(n)}是已知數列，n≧1。
我們得知當正項級數sum_{n=1}^infinity c_(n)收斂，則有有界解存在，且皆為單調。
而正項級數sum_{n=1}^infinity c_(n)發散，則沒有無界解。
最後我們討論當sum_{n=1}^infinity c_(n)不是正項級數時，解的存在及行為。

關鍵字

差分方程式

並列摘要

For sequence , {c_(n)}, we consider the following difference equation.
a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2-S^2}.
We will apply the method of backward induction to establish the existence, the uniqueness and behavior of the solution under certain conditions.
We know that the difference equation has bounded monotone solution if the positive series sum_{n=1}^infinity c_(n) is convergent.
However, the difference equation has no unbounded solution if the positive series sum_{n=1}^infinity c_(n) is divergent.
Finally, we consider the existence, the uniqueness and behavior of the solution of the difference equation under sum_{n=1}^infinity c_(n) is not positive series.

並列關鍵字

Difference Equations

參考文獻

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[7] P.P. Korovkin, On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR , 90 (1953) pp. 961-964 (In Russian).

參考文獻：

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