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Improvements of Hermite-Hadamard-Mercer inequality using k-fractional integral
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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.
Title: Improvements of Hermite-Hadamard-Mercer inequality using k-fractional integral
Description:
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.
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