• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.469-485
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• 2021

In this paper, some new classes of the higher order strongly exponentially preinvex functions are introduced. New relationships among various concepts of higher order strongly exponentially preinvex functions are established. It is shown that the optimality conditions of differentiable higher order strongly exponentially preinvex functions can be characterized by exponentially variational-like inequalities. Parallelogram laws for Banach spaces are obtained as an application. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previously known results.