Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method

Abstract

In this paper, new refinements and improvements of Mitrinovic–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish new bounds for Mitrinovic–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sandor’s inequalities. The analysis results show that our bounds are tighter than the previous methods.