Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions
Miguel José Vivas Cortez, Pontificia Universidad Católica del Ecuador, Facultad de Ciencias Naturales y Exactas, Escuela de Ciencias Físicas y Matemáticas, Sede Quito, Ecuador, Muhammad Aamir Ali, Artion Kashuri, Hüseyin Budak
Abstract
<abstract> In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, $ k $-Riemann-Liouville ($ k $-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel. </abstract>