Open AccessSome Remarks on Results Related to ∇-Convex Function
Author(s) -
Asif R. Khan,
Faraz Mehmood,
Faisal Nawaz,
Aamzir
Publication year - 2021
Publication title -
journal of mathematical and fundamental sciences/journal of mathematical and fundamental siences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 12
eISSN - 2337-5760
pISSN - 2338-5510
DOI - 10.5614/j.math.fund.sci.2021.53.1.5
Subject(s) - mathematics , generalization , differentiable function , type (biology) , mean value theorem (divided differences) , order (exchange) , pure mathematics , convex function , regular polygon , function (biology) , mathematical analysis , picard–lindelöf theorem , fixed point theorem , ecology , geometry , finance , evolutionary biology , economics , biology
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.