Research article

Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals

  • Received: 25 April 2020 Accepted: 11 June 2020 Published: 15 June 2020
  • MSC : 26A33, 26A51, 26D07, 26D10, 26D15

  • Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville k-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville k-Fractional integral inequalities. We also give Ψ-Riemann-Liouville k-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.

    Citation: Saad Ihsan Butt, Artion Kashuri, Muhammad Umar, Adnan Aslam, Wei Gao. Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals[J]. AIMS Mathematics, 2020, 5(5): 5193-5220. doi: 10.3934/math.2020334

    Related Papers:

  • Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville k-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville k-Fractional integral inequalities. We also give Ψ-Riemann-Liouville k-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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