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Advances in Mathematical Inequalities and Applications pp 71–89Cite as

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A New Class of Generalized Convex Functions and Integral Inequalities

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Abstract

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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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Mohamed Jleli & Bessem Samet

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Mohamed Jleli
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  2. Donal O’Regan
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  3. Bessem Samet
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Corresponding author

Correspondence to Bessem Samet .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  2. Department of Mathematics, Victoria University, Melbourne, VIC, Australia

    Silvestru Sever Dragomir

  3. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

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Jleli, M., O’Regan, D., Samet, B. (2018). A New Class of Generalized Convex Functions and Integral Inequalities. In: Agarwal, P., Dragomir, S., Jleli, M., Samet, B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-3013-1_4

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