Some Remarks on Results Related to ∇-Convex Function

Some Remarks on Results Related to ∇-Convex Function

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 varia...

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Bibliographic Details
Main Authors: Asif Raza Khan, Faraz Mehmood, Faisal Nawaz, Aamna Nazir
Format: Article
Language:English
Published: ITB Journal Publisher 2021-05-01
Series:Journal of Mathematical and Fundamental Sciences
Subjects:
convex function
∇-convex function
∇-operator
divided difference of a function
finite difference of a function
Online Access:https://journals.itb.ac.id/index.php/jmfs/article/view/9061
Description
Summary: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.
ISSN:2337-5760
2338-5510

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