Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus

被引：5

作者：

Stojiljkovic, Vuk ^{[1
]}

Radojevic, Slobodan ^{[2
]}

Cetin, Eyup ^{[3
,4
]}

Cavic, Vesna Sesum ^{[5
]}

Radenovic, Stojan ^{[2
]}

机构：

[1] Univ Novi Sad, Fac Sci, Trg Dositeja Obradovica 3, Novi Sad 21000, Serbia

[2] Univ Belgrade, Fac Mech Engn, Kraljice Marije 16, Belgrade 11120, Serbia

[3] York Univ, Lab Ind & Appl Math, Toronto, ON M3J 1P3, Canada

[4] New York Business Global, 9591 Baltimore Ave 703, College Pk, MD 20741 USA

[5] Univ Belgrade, Gradevinski Fak, Bulevar Kralja Aleksandra 73, Belgrade 11000, Serbia

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 06期

关键词：

polynomial bounds; L'Hopital's rule of monotonicity; Jordan's inequality; trigonometric functions;

D O I：

10.3390/sym14061260

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral.

引用

页数：9

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