SOME NEW GENERALIZATIONS OF HADAMARD–TYPE MIDPOINT INEQUALITIES INVOLVING FRACTIONAL INTEGRALS
| Autor: | Bahtiyar Bayraktar |
|---|---|
| Přispěvatelé: | Bursa Uludağ Üniversitesi/Eğitim Fakültesi., Bayraktar, Bahtiyar |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Inequality Applied Mathematics media_common.quotation_subject h¨older’s inequality Hadamard inequality Type (model theory) Midpoint Convexity Holder's inequality Hadamard transform Ostrowski Type Inequality Convex Function Fractional Integral riemann–liouville fractional integrals QA1-939 power–mean inequality Power-mean inequality Riemann-Liouville fractional integrals Mathematics Analysis media_common |
| Zdroj: | Проблемы анализа, Vol 927, Iss 3, Pp 66-82 (2020) |
| ISSN: | 2306-3432 |
| DOI: | 10.15393/j3.art.2020.8270 |
| Popis: | In this study, we formulate the identity and obtain some generalized inequalities of the Hermite-Hadamard type by using fractional Riemann-Liouville integrals for functions whose absolute values of the second derivatives are convex. The results are obtained by uniformly dividing a segment [a,b] into n equal sub-intervals. Using this approach, the absolute error of a Midpoint inequality is shown to decrease approximately n(2) times. A dependency between accuracy of the absolute error (epsilon) of the upper limit of the Hadamard inequality and the number (n) of lower intervals is obtained. |
| Databáze: | OpenAIRE |
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