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New converses of Levinson's type inequality and Levinson's type generalization of Jensen-Mercer's inequality in time scale settings

In this paper we obtain Levinson's type inequality on time scale by using a new class of functions that has been recenty introduced by Baloch, Pe\v{;c};ari\'{;c}; and Praljak. The authors proved that is the largest class of functions for which Levinson's inequality hold under Mecer's assumptions. We obtain new converses of Levinson's type inequality on time scale, as well as Levinson's type generalization of Jensen-Mercer's inequality on time scale.

Levinson's inequality, Jensen's inequality, time scale calculus

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