Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity...

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Published inSymmetry (Basel) Vol. 13; no. 12; p. 2249
Main Authors Ali, Muhammad Aamir, Kara, Hasan, Tariboon, Jessada, Asawasamrit, Suphawat, Budak, Hüseyin, Hezenci, Fatih
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2021
Subjects
Convex analysis
Fractional calculus
Inequalities
Inequality
Integrals
Operators (mathematics)
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Summary:From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym13122249