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    q-Hermite-Hadamard Inequalities for Generalized Exponentially (s, m; eta)-Preinvex Functions
    (Hindawi Ltd, 2021) Wang, Hua; Kalsoom, Humaira; Budak, Hüseyin; Idrees, Muhammad
    In this article, we introduce a new extension of classical convexity which is called generalized exponentially (s, m; eta)-preinvex functions. Also, it is seen that the new definition of generalized exponentially (s, m; eta)-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new (m kappa 2)q-integral identity for the twice (m kappa 2)q-differentiable function. By using this identity, we show essential new results for Hermite-Hadamard-type inequalities for the (m kappa 2)q-integral by utilizing differentiable exponentially (s, m; eta)-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.