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Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators

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Abstract

Since the so-called Hermite–Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite–Hadamard–Fejér type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the known generalized fractional integral operators. We also point out that certain known inequalities are particular cases of the results presented here.

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Acknowledgements

This research is supported by Ordu University Scientific Research Projects Coordination Unit (BAP). Project Number: B-1809.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey

    Erhan Set & E. Aykan Alan

  2. Department of Mathematics, Dongguk University, Gyeongju, 38066, Republic of Korea

    Junesang Choi

Authors
  1. Erhan Set
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  2. Junesang Choi
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  3. E. Aykan Alan
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Correspondence to Junesang Choi.

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Erhan Set declares that he has no conflict of interest. Junesang Choi declares that he has no conflict of interest. E. Aykan Alan declares that he has no conflict of interest.

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Set, E., Choi, J. & Alan, E.A. Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators. J Anal 27, 1007–1027 (2019). https://doi.org/10.1007/s41478-018-0159-5

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  • DOI: https://doi.org/10.1007/s41478-018-0159-5

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