\(q\)-Hermite-Hadamard inequalities for generalized exponentially \((s,m;\eta)\)-preinvex functions (Q2036040)

Summary: 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.