On q-Hermite–Hadamard inequalities for general convex functions

Abstract

The Hermite–Hadamard inequality was first considered for convex functions and has been studied extensively. Recently, many extensions were given with the use of general convex functions. In this paper we present some variants of the Hermite–Hadamard inequality for general convex functions in the context of q-calculus. From our theorems, we deduce some recent results in the topic.

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Acknowledgement

The authors thank the anonymous referee for useful suggestions to improve the presentation of the results.

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Correspondence to P. Kórus.

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Bermudo, S., Kórus, P. & Nápoles Valdés, J.E. On q-Hermite–Hadamard inequalities for general convex functions. Acta Math. Hungar. 162, 364–374 (2020). https://doi.org/10.1007/s10474-020-01025-6

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Key words and phrases

  • Hermite–Hadamard inequality
  • q-integral inequality
  • q-calculus
  • h-convex function
  • modified h-convex function

Mathematics Subject Classification

  • 26D10
  • 26D15
  • 26A33