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 Mitrinović–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 Mitrinović–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sándor’s inequalities. The analysis results show that our bounds are tighter than the previous methods.

Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions

“…For different refinements, generalizations, and recent developments regarding inequalities involving the sinc and hyperbolic sinc functions, we refer the reader to [2][3][4][5]7,12,13,17,[21][22][23][24][25][26]. This article aims to present new generalized bounds for sinc and hyperbolic sinc functions.…”