Discrete Inequalities of Steffensen and Hayashi Type in Inner Product Spaces with Applications

Marek Niezgoda


In this paper, a unified approach to Steensen and Hayashi type inequalities in inner product spaces is presented. Single and double Steensen–Hayashi type inequalities are established. In particular, some refinements and extensions of the classical results from [J. C. Evard and H. Gauchman, Steffensen type inequalities over general measure spaces, Analysis, 17 (1997), 301-322] and [H.-N. Shi and S.-H.Wu, Majorized proof and improvement of the discrete Steffensen’s inequality, Taiwanese J. Math., 11 (2007) 1203-1208] are demonstrated. Applications are provided to bounding expectations of discrete random variables.

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