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

• Main Authors: Yu-Dian Tasi, 蔡育典
• Other Authors: 陳功宇
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/86791135148341087296

碩士 === 淡江大學 === 數學學系碩士班 === 99 === 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.