Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910299188101120 |
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| author | Goswami, Angshuman R. Hartung, Ferenc |
| author_facet | Goswami, Angshuman R. Hartung, Ferenc |
| contents | A convex function $f:[a,b]\to\mathbb{R}$ satisfies the so-called Hermite-Hadamard inequality $$ f\left(\frac{a+b}{2}\right)\leq \frac{1}{b-a}\int_a^{b}f(t)dt\leq \frac{f(a)+f(b)}{2}. $$ 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 $\frac1{b-a}\mathcal{I}_{n}(f)$, where $\mathcal{I}_{n}(f)$ denotes some of the most popular Newton-Cotes quadrature formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas Goswami, Angshuman R. Hartung, Ferenc General Mathematics 26A48, 26A51, 65D30 A convex function $f:[a,b]\to\mathbb{R}$ satisfies the so-called Hermite-Hadamard inequality $$ f\left(\frac{a+b}{2}\right)\leq \frac{1}{b-a}\int_a^{b}f(t)dt\leq \frac{f(a)+f(b)}{2}. $$ 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 $\frac1{b-a}\mathcal{I}_{n}(f)$, where $\mathcal{I}_{n}(f)$ denotes some of the most popular Newton-Cotes quadrature formulas. |
| title | Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas |
| topic | General Mathematics 26A48, 26A51, 65D30 |
| url | https://arxiv.org/abs/2401.08620 |