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q-Hermite–Hadamard Inequalities for Generalized Exponentially s,m;η-Preinvex Functions

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  • Hua Wang
  • Humaira Kalsoom
  • Hüseyin Budak
  • Muhammad Idrees
  • Ahmet Ocak Akdemir

Abstract

In this article, we introduce a new extension of classical convexity which is called generalized exponentially s,m;η-preinvex functions. Also, it is seen that the new definition of generalized exponentially s,m;η-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new qmκ2-integral identity for the twice qmκ2-differentiable function. By using this identity, we show essential new results for Hermite–Hadamard-type inequalities for the qmκ2-integral by utilizing differentiable exponentially s,m;η-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.

Suggested Citation

  • Hua Wang & Humaira Kalsoom & Hüseyin Budak & Muhammad Idrees & Ahmet Ocak Akdemir, 2021. "q-Hermite–Hadamard Inequalities for Generalized Exponentially s,m;η-Preinvex Functions," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, April.
    • Handle: RePEc:hin:jjmath:5577340
    DOI: 10.1155/2021/5577340
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