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
Part of the Trends in Mathematics book series (TM)


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.


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

2010 Mathematics Subject Classification

26A51 26D15 



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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© 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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