Some Remarks on Results Related to ∇-Convex Function
Asif R. KhanDepartment of Mathematics, University of Karachi, University Road, Karachi 75270, PakistanFaraz MehmoodDepartment of Mathematics, Dawood University of Engineering and Technology, New M.A. Jinnah Road, Karachi 74800, PakistanFaisal NawazDepartment of Mathematics, Dawood University of Engineering and Technology, New M.A. Jinnah Road, Karachi 74800, PakistanAamna NazirDepartment of Mathematics, University of Karachi, University Road, Karachi 75270, Pakistan
2021en
ABI
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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