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New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators

Author

Listed:
  • Qiong Kang
  • Saad Ihsan Butt
  • Waqas Nazeer
  • Mehroz Nadeem
  • Jamshed Nasir
  • Hong Yang
  • Sei-Ichiro Ueki

Abstract

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.

Suggested Citation

  • Qiong Kang & Saad Ihsan Butt & Waqas Nazeer & Mehroz Nadeem & Jamshed Nasir & Hong Yang & Sei-Ichiro Ueki, 2020. "New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators," Journal of Mathematics, Hindawi, vol. 2020, pages 1-14, August.
    • Handle: RePEc:hin:jjmath:4303727
    DOI: 10.1155/2020/4303727
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