The Hermite-Hadamard inequality has been recognized as the most pivotal which grabbed attention of several mathematicians. In recent years, load results have established for this inequality. main theme article is to present generalized via Jensen-Mercer and majorization concept. We establish a type majorized tuples. With aid weighted Mercer?s inequality, we also prove certain idea obtaining pap...

Throughout, X stands for a real Banach space, SX for its unit sphere, X ∗ for its topological dual, and 〈·, ·〉 for the duality pairing. All the functions f : X → R∪{+∞} are lower semicontinuous. The Clarke subdifferential , the Hadamard subdifferential and the Fréchet subdifferential of f are respectively denoted by ∂Cf , ∂Hf and ∂F f . The Zagrodny two points mean value inequality has proved t...

holds. This double inequality is known in the literature as Hermite-Hadamard integral inequality for convex functions. Note that some of the classical inequalities for means can be derived from (1.1) for appropriate particular selections of the mapping f . Both inequalities hold in the reversed direction if f is concave. For some results which generalize, improve and extend the inequalities (1....

hold. This double inequality is known in the literature as the Hermite–Hadamard inequality for convex functions. In recent years many authors established several inequalities connected to this fact. For recent results, refinements, counterparts, generalizations and new Hermite-Hadamard’stype inequalities see [1]–[18]. We recall that the notion of quasi-convex function generalizes the notion of ...

Abstract In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex functions by using Riemann–Liouville fracti...

We establish Hadamard-type inequalities for a class of symmetric matrices called $k$-positive which the $m$-th elementary functions their eigenvalues are positive all $m\leq k$. These arise naturally in study $k$-Hessian equations Partial Differential Equations. For each matrix, we show that sum its principal minors size $k$ is not larger than $k$-th function diagonal entries. The case $k=n$ co...

Abstract In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for integrals. The results obtained are applied fractional integrals various and therefore contain previous reported in the literature.

Abstract In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for case quasi-arithmetically convex (q-ac) functions which acts as a generator all quasi-arithmetic means in frame work integral.