Foundations (Jun 2023)

A Comprehensive Review of the Hermite–Hadamard Inequality Pertaining to Quantum Calculus

  • Muhammad Tariq,
  • Sotiris K. Ntouyas,
  • Asif Ali Shaikh

DOI
https://doi.org/10.3390/foundations3020026
Journal volume & issue
Vol. 3, no. 2
pp. 340 – 379

Abstract

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A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety of classes of convexities, is presented. In the various classes of convexities this includes classical convex functions, quasi-convex functions, p-convex functions, (p,s)-convex functions, modified (p,s)-convex functions, (p,h)-convex functions, tgs-convex functions, η-quasi-convex functions, ϕ-convex functions, (α,m)-convex functions, ϕ-quasi-convex functions, and coordinated convex functions. Quantum H-H type inequalities via preinvex functions and Green functions are also presented. Finally, H-H type inequalities for (p,q)-calculus, h-calculus, and (q−h)-calculus are also included.

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