Hermite-Hadamard Type Inequalities Research Articles

Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

Abstract In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.

SOME HERMITE-HADAMARD TYPE INEQUALITIES INVOLVING FRACTIONAL INTEGRAL OPERATORS

The aim of this article is to give new generalized Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral for functions whose absolute values of third derivatives are s-convex in the second sense. In order to do that an integral identity for three times differentiable mapping involving fractional integral operators is established. Several consequences are then presented in some special cases.

On q-Hermite-Hadamard Inequalities via q − h-Integrals

This paper aims to find Hermite–Hadamard-type inequalities for a generalized notion of integrals called q−h-integrals. Inequalities for q-integrals can be deduced by taking h=0 and are connected with several known results of q-Hermite–Hadamard inequalities. In addition, we analyzed q−h-integrals, q-integrals, and the corresponding inequalities for symmetric functions.

Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function

Abstract In this paper, first we define interval-valued left-sided and right-sided fractional integrals of a function with respect to the another function. Then, we handle Hermite-Hadamard type inequalities via these definitions.

Mappings related to Hermite-Hadamard type inequalities for harmonically convex functions

In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.

Some Hermite–Hadamard type inequalities for GA‐s‐convex functions in the fourth sense

In the present manuscript, we define the concept of ‐ ‐convex functions in the fourth sense. We obtain the Hermite–Hadamard inequality for the newly introduced class of functions. We also establish some inequalities of the Hermite–Hadamard type for functions whose first derivative in absolute value at certain powers is a ‐ ‐convex function in the fourth sense. In the last, some applications to special means of real numbers are given.

Hermite–Hadamard type inequality for (E, F)-convex functions and geodesic (E, F)-convex functions

The main aim of the present paper is to introduce geodesic (E, F)-convex sets and geodesic (E, F)-functions on a Riemannian manifold. Furthermore, some basic properties of these mappings are investigated. Moreover, the Hadamard-type inequalities for (E, F)-convex functions are proven.

On the Generalized Inequalities for Co-Ordinated Convex Functions

Abstract The aim of this paper is to establish some generalized integral inequalities for convex functions of 2-variables on the co-ordinat. Then, we will give a generalized identity and with the help of this integral identity, we will investigate some integral inequalities connected with the right hand side of the Hermite-Hadamard type inequalities involving Riemann integrals and Riemann-Liouville fractional integrals.

Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers.

On Symmetrized Stochastic Harmonically Convexity and Hermite–Hadamard Type Inequalities

Throughout this study, the concept of symmetrized harmonically convex stochastic processes will be discussed in further detail. Some certain characterizations for symmetrized harmonically convex stochastic processes are discussed that use Hermite–Hadamard-type inequalities. A Hyers–Ulam-type stability result for harmonically convex stochastic processes is given as well.

A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions

In the present paper, some Hermite-Hadamard type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions are investigated. Namely, the generalizations of the midpoint type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions in the second sense on the rectangle from the plain are established. In addition to this, it is presented several inequalities to the case of Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals by choosing the special cases of our obtained main results

Some Quantum Integral Inequalities Based on Left-Right Quantum Integrals

In this work, the concepts of quantum derivative and quantum integral were renamed to be the left quantum derivative and the left definite quantum integral. Symmetrically to the left, a new quantum derivative (the right) and definite quantum integral (the right) were defined. Some properties of these new concepts were investigated and as well as according to do these new concepts some inaccuracies in quantum integral inequalities were corrected. Moreover, some new quantum Hermite-Hadamard type inequalities were established.

Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities

The theory of convex mapping has a lot of applications in the field of applied mathematics and engineering. The fuzzy Riemann-Liouville fractional integrals are the most significant operator of fractional theory which permits to generalize the classical theory of integrals. This study considers the well-known Hermite-Hadamard type and associated inequalities. To full fill this mileage, some new versions of fuzzy Hermite-Hadamard type and Hermite-Hadamard-Fejér type inequalities for up and down convex fuzzy-number valued mappings have been obtained. Some new related fuzzy Hermite-Hadamard type inequalities are also obtained with the help of product of two up and down convex fuzzy-number valued mappings. Moreover, we have introduced some new important classes of fuzzy numbered valued convexity which are known as lower up and down convex (concave) and, upper up and down convex (concave) fuzzy numbered valued mappings by applying some mild restrictions on up and down convex (concave) fuzzy numbered valued mappings. By using these definitions, we have acquired many classical and new exceptional cases which can be viewed as applications of the main results. We also present three examples of fuzzy numbered valued convexity to demonstrate the validity of the fuzzy inclusion relations proposed in this paper.

New Hermite–Hadamard Type Inequalities in Connection with Interval-Valued Generalized Harmonically (h1,h2)-Godunova–Levin Functions

As is known, integral inequalities related to convexity have a close relationship with symmetry. In this paper, we introduce a new notion of interval-valued harmonically m,h1,h2-Godunova–Levin functions, and we establish some new Hermite–Hadamard inequalities. Moreover, we show how this new notion of interval-valued convexity has a close relationship with many existing definitions in the literature. As a result, our theory generalizes many published results. Several interesting examples are provided to illustrate our results.

Some Hermite–Hadamard and Hermite–Hadamard–Fejér Type Fractional Inclusions Pertaining to Different Kinds of Generalized Preinvexities

Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this equality as the auxiliary result, we attain some estimations of a Hermite–Hadamard type inequality involving s-preinvex, s-Godunova–Levin preinvex, and prequasi invex functions. In addition, we investigate a fractional order Hadamard–Fejér inequality and some of its refinements pertaining to h-preinvexity via a non-conformable fractional integral operator. Finally, we present a Pachpatte type inequality for the product of two preinvex functions. The findings as well as the special cases presented in this research are new and applications of our main results.

Quantum Integral Inequalities in the Setting of Majorization Theory and Applications

In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over Rn known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q˙-calculus and majorized l-tuples. Firstly we derive q˙-Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer’s inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q˙-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q˙-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper.

Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities

This study aims to connect the idea of inequalities with Riemann integral operators, which are of interest because of their characteristics and widespread use. We create a new Hermite–Hadamard type integral inequality for an

On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications

Abstract In this study, we establish some new Hermite-Hadamard type inequalities for s-convex functions in the second sense using the post-quantum calculus. Moreover, we prove a new ( p , q ) \left(p,q) -integral identity to prove some new Ostrowski type inequalities for ( p , q ) \left(p,q) -differentiable functions. We also show that the newly discovered results are generalizations of comparable results in the literature. Finally, we give application to special means of real numbers using the newly proved inequalities.

Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator

Fractional integrals and inequalities have recently become quite popular and have been the prime consideration for many studies. The results of many different types of inequalities have been studied by launching innovative analytical techniques and applications. These Hermite–Hadamard inequalities are discovered in this study using Atangana–Baleanu integral operators, which provide both practical and powerful results. In this paper, a symmetric study of integral inequalities of Hermite–Hadamard type is provided based on an identity proved for Atangana–Baleanu integral operators and using functions whose absolute value of the second derivative is harmonic convex. The proven Hermite–Hadamard-type inequalities have been observed to be valid for a choice of any harmonic convex function with the help of examples. Moreover, fractional inequalities and their solutions are applied in many symmetrical domains.

MϕA-h-Convexity and Hermite-Hadamard Type Inequalities

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