- Konuralp Journal of Mathematics
- Vol: 9 Issue: 2
- On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta ...
On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals
Authors : Seda Kilinç Yildirim, Hüseyin Budak, Hüseyin Yildirim
Pages : 356-370
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Publication Date : 2021-10-15
Article Type : Research
Abstract :In this paper, we first obtain an identity for differentiable mappings. Then we establish some new generalized inequalities for differentiable $\left( \eta _{1},\eta _{2}\right) -$ convex functions involving some parameters and generalized fractional integrals. We show that these results reduces to several new Simpson, midpoint and trapezoid type inequalities. Some special cases are also discussed.Keywords : simpson's 1/3 formula, Integral inequalities, , fractional calculus, convex functions