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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.