A basic problem of (p, q)-Bernstein-type operators

作者：Cai, Qing-Bo; Xu, Xiao-Wei^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 140.

DOI：10.1186/s13660-017-1413-0

• (p, q)-integer
• Bernstein-type approximation
• convergence theorem
• equivalent condition

In this note, we give an elaboration of a basic problem on convergence theorem of (p, q)-analogue of Bernstein-type operators. By some classical analysis techniques, we derive an exact class of (p(n), q(n))-integer satisfying lim(n ->infinity)[n](pn,) (qn) = infinity with lim(n ->infinity) p(n) = 1 and lim(n ->infinity) q(n) = 1 under 0 < q(n) < p(n) <= 1. Our results provide an erratum to corresponding results on (p, q)-analogue of Bernstein-type operators that appeared in recent literature.

• 出版日期2017-6-17
• 单位泉州师范学院; 厦门大学