A New Class of Generalized Convex Functions and Integral Inequalities

  • Mohamed Jleli
  • Donal O’Regan
  • Bessem SametEmail author
Part of the Trends in Mathematics book series (TM)


In this chapter, we introduce the class of \(\eta _\varphi \)-convex functions which is larger than the class of \(\eta \)-convex functions introduced by Gordji et al. (Preprint Rgmia Res Rep Coll 1–14, 2015 [1]). Some Fejér type integral inequalities are established for this new class of functions. As consequences, we deduce some Hermite–Hadamard type inequalities involving different kinds of fractional integrals.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland

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