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By using a Lidstone interpolation, Green’s function and Montogomery’s identity, we prove a new generalization of Steffensen’s inequality. Some related inequalities providing generalizations of certain results given in (J. Math. Inequal. 9(2):481–487,  2015 ) have also been obtained. Moreover, from these inequalities, we formulate linear functionals and describe their properties.

Generalized Steffensen’s inequality by Lidstone interpolation and Montogomery’s identity