On Parameterized Simpson, Midpoint and Trapezoid Type Inequalities for Differentiable$\ \left( \eta _{1},\eta _{2}\right) -$Convex Functions via Generalized Fractional Integrals

Year 2021, Volume: 9 Issue: 2, 356 - 370, 15.10.2021

Seda Kılınç Yıldırım , Hüseyin Budak , Hüseyin Yıldırım

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

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