A Method for Establishing Certain Trigonometric Inequalities
نویسنده
چکیده
In this note, we describe a method for establishing trigonometric inequalities that involve symmetric functions in the cosines of the angles of a triangle. The method is based on finding a complete set of relations that define the cosines of such angles.
منابع مشابه
On Certain Inequalities for Hyperbolic and Trigonometric Functions
Starting from certain inequalities for hyperbolic and trigonometric functions, we obtain some general inequalities for functions and their inverses. As applications, refinements and new inequalities for hyperbolic and trigonometric functions are pointed out.
متن کاملOn Marcinkiewicz-Zygmund-Type Inequalities
We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.
متن کاملPadé approximants for inverse trigonometric functions and their applications
The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers.
متن کاملSome New Inequalities for Trigonometric Polynomials with Special Coefficients
Some new inequalities for certain trigonometric polynomials with complex semiconvex and complex convex coefficients are given.
متن کاملBernstein Inequalities for Polynomials with Constrained Roots
We prove Bernstein type inequalities for algebraic polynomials on the finite interval I := [−1, 1] and for trigonometric polynomials on R when the roots of the polynomials are outside of a certain domain of the complex plane. The case of real vs. complex coefficients are handled separately. In case of trigonometric polynomials with real coefficients and root restriction, the Lpsituation will al...
متن کامل