Applied Mathematics & Information Sciences

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In this paper, we introduce the concept of LR-log-h-convex interval-valued functions. Under the new concept, we present new versions of Hermite-Hadamard inequalities (i.e. LR-interval Hermite-Hadamard type inequalities) by means of pseudo order relation. This order relation is defined on interval space. Some Jensen type inequalities are also derived for LR-log-h-convex interval-valued functions. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-log-h-convex interval-valued functions and their variant forms as special cases. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper will be a starting point for further research in this area.

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