New approximation inequalities for circular functions

Abstract

In this paper, we obtain some improved exponential approximation inequalities for the functions and , and we prove them by using the properties of Bernoulli numbers and new criteria for the monotonicity of quotient of two power series.

Integral Inequalities Involving Strictly Monotone Functions

“…Functional inequalities involving special functions are very useful in mathematical analysis, and several interesting results have been obtained in this topic. See e.g., [2,[15][16][17][18][19][20][21][22][23][24][25].…”

Improved bounds of Mitrinović–Adamović-type inequalities by using two-parameter functions

“…are known as Mitrinović-Adamović inequalities (see [1][2][3]). Many references [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have discussed the problems related to Eq. ( 1), such as the following power exponential inequality obtained by Nishizawa in [4] sin x x…”

Notes on a Double Inequality for Ratios of any Two Neighbouring Non-zero Bernoulli Numbers

“…is strictly increasing (or strictly decreasing, respectively) if and only if 1 θ ≤ − (or 0 θ ≥ , respectively). The double inequality (2) has been cited and applied in the papers [22][23][24][25][26][27][28][29].…”