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Novel Results on Hermite–Hadamard Kind Inequalities for \(\eta \)-Convex Functions by Means of (kr)-Fractional Integral Operators

  • Eze R. Nwaeze
  • Delfim F. M. TorresEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

We establish new integral inequalities of Hermite–Hadamard type for the recent class of \(\eta \)-convex functions. This is done via generalized (kr)-Riemann–Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters k and r, one obtains interesting new results.

Keywords

Hermite–Hadamard inequalities \(\eta \)-convexity Riemann–Liouville integrals 

2010 Mathematics Subject Classification

26A51 26D15 

Notes

Acknowledgements

This research was supported by FCT and CIDMA, project UID/MAT/04106/2013. The authors are grateful to the referees for their valuable comments and helpful suggestions.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsTuskegee UniversityTuskegeeUSA
  2. 2.CIDMA, Department of MathematicsUniversity of AveiroAveiroPortugal

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