The natural algorithmic approach of mixed trigonometric-polynomial problems

Abstract

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to analyze some new rational (Pade) approximations of the function ${\cos }^2(x)$, and to improve a class of inequalities by Z.-H. Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.

References in corpus (6)

• On Jordan type inequalities for hyperbolic functions
• A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions
• Accurate approximations of some expressions involving trigonometric functions
• Some notes on a method for proving inequalities by computer
• A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions
• New sharp Jordan type inequalities and their applications

Cited by in corpus (9)

• Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities
• Sharpening and Generalizations of Shafer-Fink and Wilker Type Inequalities: a New Approach
• About some exponential inequalities related to the sinc function
• Refined estimates and generalizations of inequalities related to the arctangent function and Shafer's inequality
• One method for proving some classes of exponential analytic inequalities
• Exponential Polynomials and Stratification in the Theory of Analytic Inequalities
• Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems
• Some improvements of Jordan-Steckin and Becker-Stark inequalities
• Wilker and Huygens type inequalities for mixed trigonometric-hyperbolic functions