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

  • Erhan Set
  • Junesang Choi
  • E. Aykan Alan
Original Research Paper
  • 10 Downloads

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.

Keywords

Convex function Quasi-convex function Symmetrized convex function Wright-quasi-convex functions Hermite–Hadamard type inequalities Generalized fractional integral operators Hermite–Hadamard–Fejér type inequalities 

Mathematics Subject Classification

26A33 26D10 26D15 33B20 

Notes

Acknowledgements

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

Compliance with ethical standards

Human participants or animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Conflict of interest

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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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and ArtsOrdu UniversityOrduTurkey
  2. 2.Department of MathematicsDongguk UniversityGyeongjuRepublic of Korea

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