期刊论文

Chu, Yu-Ming

英文

Mathematical Problems in Engineering

1024-123X

2016

2016

1-5

10.1155/2016/1579468

Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61374086, 11371125, 11401191]; Natural Science Foundation of Zhejiang Broadcast and TV University [XKT-15G17]

本校为通讯机构

We prove that the double inequality J α ( a , b ) < U ( a , b ) < J β ( a , b ) holds for all a , b > 0 with a ≠ b if and only if α ≤ 2 / ( π - 2 ) = 0.8187 ⋯ and β ≥ 3 / 2 , where U ( a , b ) = ( a - b ) / [ 2 arctan ⁡ ( ( a - b ) / 2 a b ) ] , and J p ( a , b ) = p ( a p + 1 - b p + 1 ) / [ ( p + 1 ) ( a p - b p ) ] ( p ≠ 0 , - 1 ) , J 0 ( a , b ) = ( a - b ) / ( log ⁡ a - log ⁡ b ) , and J - 1 ( a , b ) = a b ( log ⁡ a - log ⁡ b ) / ( a - b ) are the Yang and p...