Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions
Muhammad Aamir Ali, Jarunee Soontharanon, Hüseyin Budak, Thanin Sitthiwirattham, Mičhal Fĕckan
Abstract
In this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Ho & BULL;lder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.