Improvements of Hermite-Hadamard-Mercer inequality using k-fractional integral

The well-known Hermite-Hadamard inequality has attracted the attention of several researchers due to the fact that Hermite-Hadamard inequality has many important applications in mathematics as well as in other areas of science. In this article, the authors present new Hermite-Hadamard inequality of the Mercer type containing Riemann-Liouville k-fractional integrals. For these inequalities, we give integral identity for differentiable functions. With the help of the identity and Hermite-Hadamard-Mercer type inequalities, we derive several results for the inequalities. We establish bounds for the difference of the obtain results by applying Hölder's inequality and power-mean inequality. We hope that the proposed result will invigorate further interest in this direction.