Refinements and generalizations of some inequalities of Shafer-Fink’s type for the inverse sine function

Abstract

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink’s inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017).

Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach

“…1− • For n = 4 we have : • For n = 5 we have : • For n = 6 we have : In [11] the authors proved the following assertion. for m ∈ N, m 2 E(1) = 0 .…”

“…In this paper, concerning Shafer-Fink's inequality, we propose and prove some extensions of Theorems 1 and 2 from [11].…”

Inequalities and asymptotic expansions related to the generalized Somos quadratic recurrence constant

“…Using the methods from [20–22] it is possible to get estimations (based on the power series expansions) of the logarithm function that can be used, for example, in the analysis of parameterized Euler-constant function, which will be an item for further work.…”

Approximating trigonometric functions by using exponential inequalities

“…Inequalities involving trigonometric and inverse trigonometric functions play an important role and have many applications in science and engineering [2,8,12,[17][18][19]27]. The sinc function, defined as sin(x)…”

“…Later, the sinc function is bounded by using polynomials [7,10,17,24], or by using exponential bounds [3,4,25]. Cusa-Huygens's inequality is studied in [3,4,11,20,22,23,25], and gives…”