The multi-parameterized integral inequalities for multiplicative Riemann-Liouville fractional integrals. (English) Zbl 07922179
Summary: Using the multiplicative Riemann-Liouville fractional integrals, for \(^{\ast \ast}\)differentiable functions, we present a fractional integral identity together with multi-parameters. Relying on it, and the fact that the function \(f^{\ast \ast}\) is multiplicatively convex or \((\ln f^{\ast \ast})^q\) is convex for \(q > 1\), in particular considering the case \(0 < q \leq 1\), a series of three-point Newton-Cotes type inequalities are obtained in this article. To enable the readers to comprehend the results better, we provide three examples to support the findings obtained here. Some applications in special means are offered as well.
MSC:
| 26Dxx | Inequalities in real analysis |
| 26Axx | Functions of one variable |
| 34Axx | General theory for ordinary differential equations |
Keywords:
Hermite-Hadamard-type inequalities; multiplicative Riemann-Liouville fractional integrals; \(^{\ast \ast}\) differentiable functionsReferences:
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