# Some Remarks on Results Related to ?-Convex Function

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2021.53.1.5## Keywords:

convex function, ?-convex function, ?-operator, divided difference of a function, finite difference of a function## Abstract

In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ?-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented.

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