Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus

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Abstract

The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval [b0, b1 ] ⊂ ℜ, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at b0 ∈ [b0, b1 ] ⊂ℜ. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point b1, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus.

Original languageEnglish
Pages (from-to)5523-5549
Number of pages27
JournalAIMS Mathematics
Volume9
Issue number3
DOIs
StatePublished - 2024

Keywords

  • convex functions
  • Hermite-Hadamard inequality
  • symmetric quantum calculus

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