A new refined form of Jordan’s inequality and its applications

A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality, II

“…Specially, putting (τ, λ) = (2, 2) and (τ, λ) = (1, 2) in Corollary 2 respectively yields the main results of previous papers due to Zhu [2,3] andÖzban, [4], that is…”

“…Inequality (16) is the main result of our recent paper [9], which is also a unified generalization of the earlier results of many authors (see [2][3][4][5]13].…”

“…Considerable attention has been given to the Yang Le inequality by many authors, and it has been generalized and extended in different directions (see [2][3][4][5]). We give here a new improvement of the Yang Le inequality.…”

“…This simple inequality has motivated a large number of research papers concerning its new proofs, various generalizations, sharpness and applications (e.g., see Zhu [2,3],Özban [4], Debnath and Zhao [5], Yuefeng [6], Wu [7], Mercer et al [8]). In a recent paper Wu and Debnath [9] established the following sharp lower and upper bounds for the function ( sin x x ) as an improvement of Jordan's inequality…”

An identity related to Jordan′s inequality

“…with equality holds if and only if x = π/2 (see [2,4,6]). The inequality (1.3) is slightly stronger than the inequality (1.2) and is sharp in the sense that 1/π 3 cannot be replaced by a larger constant.…”