A Sharp Double Inequality Involving Trigonometric Functions and Its Applications
نویسندگان
چکیده
We present the best possible parameters p,q ∈ (0,1] such that the double inequality 1 3p2 cos(px)+ 1− 1 3p2 < sin(x) x < 1 3q2 cos(qx)+ 1− 1 3q2 holds for all x ∈ (0,π/2) . As applications, some new inequalities for the sine integral, Catalan constant and Schwab-Borchardt mean are found. Mathematics subject classification (2010): 26D05, 26E60.
منابع مشابه
A Class of Completely Monotonic Functions Involving Divided Differences of the Psi and Polygamma Functions and Some Applications
A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...
متن کاملSharp Jackson-type Inequalities for Approximations of Classes of Convolutions by Entire Functions of Exponential Type
In this paper, a new method is introduced for the proof of sharp Jacksontype inequalities for approximation of convolution classes of functions defined on the real line. These classes are approximated by linear operators with values in sets of entire functions of exponential type. In particular, a sharp Jackson-type inequality for the even-order derivatives of the conjugate function is proved. ...
متن کاملOptimization with Positive Trigonometric Polynomials: a Review and New Applications
This paper has a double purpose. Firstly, we review recent results regarding the characterization of positive multivariate trigonometric polynomials as functions of sumof-squares polynomials. Using the linear matrix inequality parameterization of sum-of-squares, we discuss several optimization applications, among which the design of 2D FIR filters with linear or nonlinear phase. Secondly, we pr...
متن کاملA Sharp Jackson Inequality for Best Trigonometric Approximation
The paper presents a sharp Jackson inequality and a corresponding inverse one for best trigonometric approximation in terms of moduli of smoothness that are equivalent to zero on the trigonometric polynomials up to a certain degree. Sharp relations between such moduli of different order are also considered.
متن کاملComputation of Trigonometric Functions by the Systolic Implementation of the CORDIC Algorithm
Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016