Vivas-Cortez, MiguelAli, Muhammad AamirKashuri, ArtionBudak, Huseyin2021-12-012021-12-0120212473-6988https://doi.org/10.3934/math.2021546https://hdl.handle.net/20.500.12684/10794In 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.en10.3934/math.2021546info:eu-repo/semantics/openAccessHermite-Hadamard inequalityHermite-Hadamard-Mercer inequalityHolder inequalityJensen-Mercer inequalityconvex functionsfractional integralsIntegral-InequalitiesDifferentiable MappingsReal NumbersArticle69939794212-s2.0-85108365098WOS:000685892800017Q2Q1