Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas

2023/12/05 by Angshuman R. Goswami, Goswami, Angshuman R., Ferenc Hartung +1
Mathematics · #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2401.08620

Abstract

A convex function f:[a,b]→ℝ satisfies the so-called Hermite-Hadamard inequality f((a+b)/(2))≤ (1)/(b-a)∫_a^bf(t)dt≤ (f(a)+f(b))/(2). Motivated by the above estimates, in this paper we consider approximately monotone and convex functions, and give upper and lower bounds to the numerical integral mean, i.e., to \frac1b-aI_n(f), where I_n(f) denotes some of the most popular Newton-Cotes quadrature formulas.

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