The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from our results by choosing different values of $n\in\mathbb{N}.$ Furthermore, we add to the literature a new result for positive functions convex on the coordinates.
In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann-Liouville and the Hadamard fractional integrals into a single form. We prove that, in most cases, we obtain the Riemann--Liouville and the Hadamard equivalence just by taking limits when a parameter $ρ\rightarrow 1$ and $ρ\rightarrow 0^+$, respectively.
In literature the Hermite-Hadamard inequality was eligible for many reasons, one of the most surprising and interesting that the Hermite-Hadamard inequality combine the midpoint and trapezoid formulae in an inequality. In this work, a Hermite-Hadamard like inequality that combines the composite trapezoid and composite midpoint formulae is proved. So that, the classical Hermite-Hadamard inequality becomes a special case of the presented result. Some Ostrowski's type inequalities for convex functions are proved as well.
The author introduces the concept of harmonically (α,m)-convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.
In this paper, Hermite-Hadamard type inequality for Sugeno integrals based on log-convex functions is studied. Some examples are given to illustrate the results.
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
The main goal of this paper is to prove a Hermite-Hadamard type inequality for certain Schur convex functions using, as one of the main tools in the proof, a Korovkin-type approximation theorem.
In this paper, we establish a new refinement of the right-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices.
In this paper, we establish a new refinement of the left-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices.
Authors introduce the concept of harmonically $(s,m)$-convex functions in second sense in \cite{II}.In this article, we establish some Hermite-Hadamard type inequalities of this class of functions.
We establish some new inequalities of Hermite-Hadamard type for functions whose fourth derivatives absolute values are quasi-convex. Further, we give new identity.Using this new identity, we establish similar inequalities for left-hand side of Hermite-Hadamard result.Also, we present applications to special means.
Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.
In this paper, we established Hermite-Hadamard-Fejer type inequalities for s-convex functions in the second sense via fractional integrals. The some results presented here would provide extansions of those given in earlier works.
In this paper, we consider a new class of convex functions which is called $λ$-preinvex functions. We prove several Hermite-Hadamard type inequalities for differentiable $λ$-preinvex functions via Fractional Integrals. Some special cases are also discussed.
We give new necessary and sufficient conditions for higher order convex ordering. These results generalize the Levin-Stečkin theorem (1960) on convex ordering. The obtained results can be useful in the study of the Hermite-Hadamard type inequalities and in particular inequalities between the quadrature operators.
We establish a new refinement of the right-hand side of the Hermite-Hadamard inequality for simplices, based on the average values of a convex function over the faces of a simplex and over the values at their barycenters.
We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here for a wide class of convex functions, but not in general. Some supplementary results are also given.
In this paper, we consider a new class of convex functions which is called $h_φ-$preinvex functions. We prove several Hermite--Hadamard type inequalities for differentiable $h_φ$-preinvex functions via Fractional Integrals. Some special cases are also discussed. Our results extend and improve the corresponding ones in the literature.
In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality. The results presented here would provide extensions of those given in earlier works.
In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and $q-$special functions are also pointed out.
A function $f:[a,b] \rightarrow \mathbb{R}$ is called $(p,a,b)$-convex if $f$ is $p$ times continuously differentiable, $f^{(p)}$ is convex and increasing, and $f^{(k)}(a)=0$ for all $k=1,\ldots,p$ where $f^{(j)}$ is the $j$th derivative of $f$. In this note we prove Hermite-Hadamard inequalities for $(p,a,b)$-convex functions that are significantly tighter than the classical Hermite-Hadamard inequality. We also prove inequalities for fractional integrals that involve $(p,a,b)$-convex functions.
In the paper, two new identities involving the local fractional integrals have been established. Using these two identities, we obtain some generalized Hermite-Hadamard type integral inequalities for the local differentiable generalized convex functions.
In \cite{II}, authors introduced the concept of harmonically $(s,m)$-convex functions in second sense which unifies different type of convexities and is more general notion of Harmonic convexity. In this paper, authors obtain new estimates on generalization of Hermite-Hadamard and Simpson type inequalities for this larger class of functions.
In this paper, it is a fuction that is a GA-convex differentiable for a new identity. As a result of this identity, some new and general integral inequalities for differentiable GA-convex functions are obtained.
In this paper, we define a new identity for twice differentiable mappings and obtained some new estimates on the generalization of Hadamard's and Simson's type inequalities for quasi-geometrically convex mappings using of this identity.
In this paper, it is a fuction that is a harmonically-convex differentiable for a new identity. As a result of this identity some new and general inequalities for differentiable harmonically-convex functions are obtained.
In this paper, some Hermite-Hadamard type inequalities are established for harmonically $(α,m)$-convex functions via fractional integrals and some Hermite-Hadamard type inequalities are obtained for these classes of functions.
We present a tight parametrical Hermite-Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value of convex function than the classical one. Our inequality becomes equality not only with affine functions, but also with a family of V-shaped curves determined by the parameter. The residual (error) of this inequality is strictly smaller than in the classical Hermite-Hadamard inequality under any probability measure and with all non-affine convex functions. In the framework of Karamata's theorem on the inequalities with convex functions, w…
We establish new integral inequalities of Hermite-Hadamard type for the recent class of $η$-convex functions. This is done via generalized $(k,r)$-Riemann-Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters $k$ and $r$, one obtains interesting new results.
