Many researchers have been attracted to the study of convex analysis theory due both facts, theoretical significance, and applications in optimization, economics, other fields, which has led numerous improvements extensions subject over years. An essential part mathematical inequalities is function its extensions. In recent past, Jensen–Mercer inequality Hermite–Hadamard–Mercer type remained a ...

We investigate a family of MϕA-h-convex functions, give some properties it and several inequalities which are counterparts to the classical such as Jensen inequality Schur inequality. weighted Hermite-Hadamard for an function estimations product two functions.

Let F be an N×N complex matrix whose jth column is the vector ~ fj in C . Let |~ fj |2 denote the sum of the absolute squares of the entries of ~ fj . Hadamard’s inequality for determinants states that | det(F )| ≤ Nj=1 |~ fj |. Here we prove a sharp upper bound on the permanent of F , which is |perm(F )| ≤ N ! NN/2 N ∏ j=1 |~ fj |, and we determine all of the cases of equality. We also discuss...

Weighted Hermite-Hadamard dual inequality in integral form is an important result as its left hand fact Jensen and right the Lah-Ribaric inequality. In this paper new linear inequalities are introduced via extension of Montgomery identity weighted with without Green functions discrete cases.

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...