New Inequalities Of Hermite Research Articles

On q-Hermite–Hadamard–Mercer and midpoint-Mercer inequalities for general convex functions with their computational analysis

This paper establishes some new inequalities of Hermite–Hadamard–Mercer type for [Formula: see text]-convex functions in the framework of [Formula: see text]-calculus and classical calculus. Some new [Formula: see text]-midpoint-Mercer type inequalities for the [Formula: see text]-differentiable [Formula: see text]-convex functions are also proved. Moreover, the computational analysis of newly established inequalities for convex and [Formula: see text]-convex functions are given to prove that the bounds of this paper are better than those of the existing ones. It is also shown with mathematical examples that the newly established inequalities are valid for [Formula: see text]-convex functions in [Formula: see text]-calculus.

Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals

Abstract In this paper, we prove some new inequalities of Hermite–Hadamard type for differentiable functions with h-convex derivatives. It is also shown that the newly established inequalities are extension of the existing inequalities in the literature. Finally, we give applications of the new results and outline some future problems.

On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus

Abstract In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature.

On Some New Inequalities of Hermite–Hadamard Midpoint and Trapezoid Type for Preinvex Functions in p,q-Calculus

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

Post-quantum Hermite\u2013Hadamard type inequalities for interval-valued convex functions

In this research, we introduce the notions of (p,q)-derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

On some inequalities for submultiplicative functions

In this work, authors establish Hermite–Hadamard inequalities for submultiplicative functions and give some more inequalities related to Hermite–Hadamard inequalities. We also give new inequalities of Hermite–Hadamard type in the special cases of our main results.

Generalized fractional integral inequalities of Hermite\u2013Hadamard type for harmonically convex functions

In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite–Hadamard type.

Some Integral Inequalities for h-Godunova-Levin Preinvexity

In this study, we define new classes of convexity called h-Godunova–Levin and h-Godunova–Levin preinvexity, through which some new inequalities of Hermite–Hadamard type are established. These new classes are the generalization of several known convexities including the s-convex, P-function, and Godunova–Levin. Further, the properties of the h-Godunova–Levin function are also discussed. Meanwhile, the applications of h-Godunova–Levin Preinvex function are given.

New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.

Hermite\u2013Hadamard type inequalities for F-convex function involving fractional integrals

In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite–Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite–Hadamard type and trapezoid type inequalities for the Riemann–Liouville fractional integrals and classical integrals.

Relative h-preinvex functions and integral inequalities

Abstract In this paper, we consider a new class of convex functions, called relative h-preivex functions. Seven new inequalities of Hermite–Hadamard type for relative h-preinvex functions are established using different approaches.

On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals.

In this paper, firstly, new Hermite–Hadamard type inequalities for harmonically convex functions in fractional integral forms are given. Secondly, Hermite–Hadamard–Fejer inequalities for harmonically convex functions in fractional integral forms are built. Finally, an integral identity and some Hermite–Hadamard–Fejer type integral inequalities for harmonically convex functions in fractional integral forms are obtained. Some results presented here provide extensions of others given in earlier works.

On Some New Inequalities of Hermite–Hadamard Type for Functions Whose Derivatives are s-Convex in the Second Sense in the Absolute Value

Several new inequalities of the Hermite–Hadamard type are established for functions whose derivatives are s-convex in the second sense in the absolute value. Some applications to special means of positive real numbers are also presented.

On new inequalities of Hermite–Hadamard–Fejér type for convex functions via fractional integrals

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–Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

Some new inequalities of Hermite–Hadamard type forn-time differentiable functions which arem-convex

In the paper, by setting up an integral identity and using Hölder integral inequality, the authors establish some new inequalities of Hermite–Hadamard type for n-time differentiable and m-convex functions and discuss applications of these inequalities to special means.