Generalization of Jensen's inequality by Euler's identity and related results
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In this paper we consider n-convex funtions. Using Euler`s identity, the result concering for Jensen`s inequality and converses of Jensen`s inequality for signed measure are presented. As a consequence, also the results concerning to the Hermite-Hadamard inequalities are presented. Using these inequlities, we produce new expenentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.
Abstract
In this paper we consider n-convex funtions. Using Euler`s identity, the result concering for Jensen`s inequality and converses of Jensen`s inequality for signed measure are presented. As a consequence, also the results concerning to the Hermite-Hadamard inequalities are presented. Using these inequlities, we produce new expenentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.
참고문헌 (13)
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