| Автор | Walsh, C. E. |
| Дата выпуска | 1940 |
| dc.description | Let f(x) ≡ (1 – x)<sup>b</sup> + b a<sup>b-1</sup> xø (x) ≡ x<sup>c</sup> – c Β<sup>c-1</sup> xwhere b ≧ 1, c ≧ 1, 0 ≦ α ≦ 1, 0 ≦ β ≦ 1, and x is assumed to lie in the range (0, 1). By differentiation, or otherwise, it is easily shewn that f(x) and ø (x) have minima when x = 1 – α and when x = β, respectively. Hence(1 – x)<sup>b</sup> + a<sup>b-1</sup> x ≧ b a<sup>b-1</sup> + (1 – b) a<sup>b</sup>x<sup>c</sup> β<sup>c-1</sup> x ≧ (1 – c)β<sup>c</sup>. |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Edinburgh Mathematical Society 1940 |
| Название | Inequalities for Positive Series |
| Тип | research-article |
| DOI | 10.1017/S0950184300002706 |
| Electronic ISSN | 0950-1843 |
| Print ISSN | 0950-1843 |
| Журнал | Edinburgh Mathematical Notes |
| Том | 32 |
| Первая страница | xxx |
| Последняя страница | xxxii |
| Аффилиация | Walsh C. E.; 34 Chelmsford Road, Ranelagh, Dublin |
