Integral Inequalities Of Hermite-Hadamard Type Research Articles

Inequalities for Hyperbolic Type Harmonic Preinvex Function

In the present paper, we have introduced a new class of preinvexity namely hyperbolic type harmonic preinvex functions and to support this new definition, some of its algebraic properties are elaborated. By using this new class of preinvexity, we have established a few Hermite-Hadamard type integral inequalities. Some novel refinements of Hemite-Hadamard type inequalities for hyperbolic type harmonic preinvex functions are presented as well. Finally, the Riemann-Liouville fractional version of the Hermite-Hadamard Inequality is established.

Hermite-Hadamard type inequalities via weighted integral operators

In this paper, we consider general convex functions of various type. We establish some new integral inequalities of Hermite-Hadamard type for (h, s, m)-convex and (h, m)-convex functions, using generalized integrals. We also investigate differentiable functions with general convex derivative. The proven results generalize many results previously known from the literature.

Hermite-Hadamard type inequalities for multiplicatively p-convex functions

In this paper, we introduced the concept of multiplicatively p-convex functions and established Hermite-Hadamard type integral inequalities in the setting of multiplicative calculus for this newly created class of functions. We also gave integral inequalities of Hermite-Hadamard type for product and quotient of multiplicatively p-convex functions. Furthermore, we obtained novel multiplicative integral-based inequalities for the product and quotient of convex and multiplicatively p-convex functions. Additionally, we derived certain upper limits for this new class of functions. The findings we proved are generalizations of the results in the literature. The results obtained in this study may inspire further research in various scientific areas.

On some integral inequalities for $(h,m)$-convex functions in a generalized framework

In this paper, we present some new integral inequalities of Hermite-Hadamard type. To obtain these results, general convex functions of various type are considered such as $(h,m)$-convex functions. The main results extend some previously known inequalities by taking fractional integral operators.

On local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) \left({\tilde{h}}_{1},{\tilde{h}}_{2}) -preinvexity involving local fractional integral operators with Mittag-Leffler kernel

Abstract Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type local fractional integral inequalities via generalized ( h ˜ 1 , h ˜ 2 ) \left({\tilde{h}}_{1},{\tilde{h}}_{2}) -preinvex function comprising local fractional integral operators and Mittag-Leffler kernel. In addition, two examples are discussed to ensure that the derived consequences are correct. As an application, we construct an inequality to establish central moments of a random variable.

Some new fractional Hermite-Hadamard type inequalities for functions with co-ordinated extended [formula omitted]-prequasiinvex mixed partial derivatives

This article introduces extended (s,m)-prequasiinvex functions on coordinates, a new form of generalized convex function. Using a previously established identity, we derive new fractional Hermite-Hadamard type integral inequalities for functions whose mixed partial derivatives belong to this new class of functions. The obtained results generalize existing Hermite-Hadamard type inequalities and have numerous applications in mathematics and physics. To demonstrate the utility of our findings, we provide examples of applications to special means, such as arithmetic, harmonic and p-logarithmic means.

Some Refinements of Hermite–Hadamard Type Integral Inequalities Involving Refined Convex Function of the Raina Type

The aim of this work is to elaborate and define the idea of refined convex function of the Raina type. In addition, we have attained some associated properties in the manner of the newly introduced idea. To add some more comprehension into the newly investigated definition, we obtain the estimations of the Hermite-Hadamard inequality. For the reader’s interest, we add some remarks regarding the Mittag-Leffer function. During the last four decades, the term Mitag-Leffler function has acquired popularity on account of its many importance in the fields of engineering and science, i.e statistical distribution theory, rheology, electric networks, fluid flow, and probability. The amazing perception regarding this function provides the solution of certain boundary value problems. The asymptotic status of this function plays a very vital performance in various problems of physics associated with fractional calculus. The methodology and amazing tools of this work may serve as an impetus for further research activities in this direction as well.

Integral inequalities of Hermite-Hadamard type for L-bounded norm weak convex mappings

Integral inequalities of Hermite-Hadamard type for L-bounded norm weak convex mappings

PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE

As a generalization of the convex mappings, the generalized [Formula: see text]-type preinvex mappings are firstly introduced. Their meaningful properties are then investigated and the Hermite–Hadamard-type integral inequalities via the newly proposed mappings in fractal space are developed. In accordance with the newly proposed identity with three parameters, it is interesting to present certain integral inequalities with regard to the mappings whose first-order derivatives in absolute value belong to the generalized [Formula: see text]-type preinvexity. As applications, on the basis of local fractional calculus, certain inequalities in view of numerical integration, [Formula: see text]-type special means, as well as moments of random variable, are acquired, respectively.

Some New Hermite-Hadamard Type Integral Inequalities for Twice Differentiable s-Convex Functions

Some New Hermite-Hadamard Type Integral Inequalities for Twice Differentiable s-Convex Functions

Hermite-Hadamard type integral inequalities for geometric-arithmetically (s,m) convex functions

In this paper, we introduce a definition of geometric-arithmetically \((s,m)\) convex function and give some new inequalities of Hermite-Hadamard type for the geometric-arithmetically \((s,m)\) convex function. Finally, we discuss applications of these inequalities to special means.

On Inequalities of Trapezium Type Via Fractional Integrals Operators

In this article, we get solutions of some integral inequalities of Hermite-Hadamard type and using the approach of ($\psi$,$h$)-Convex function by the way of Riemann-Liouville Fractional integrals and Katugampola Fractional integral operators.

Some New Quantum Hermite-Hadamard Type Inequalities for s-Convex Functions

In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities for s-convex functions by utilizing newly defined Tq-integrals. Then, by using obtained inequality, we establish a new Hermite–Hadamard inequality for coordinated s1,s2-convex functions. The results obtained in this paper provide significant extensions of other related results given in the literature. Finally, some examples are given to illustrate the result obtained in this paper. These types of analytical inequalities, as well as solutions, apply to different areas where the concept of symmetry is important.

Some New Bounds of Gauss–Jacobi and Hermite–Hadamard-Type Integral Inequalities

Some New Bounds of Gauss–Jacobi and Hermite–Hadamard-Type Integral Inequalities

Hermite-Hadamard inequalities for generalized convex functions in interval-valued calculus

<abstract> <p>The importance of convex and non-convex functions in the study of optimization is widely established. The concept of convexity also plays a key part in the subject of inequalities due to the behavior of its definition. The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this study, first, Hermite-Hadamard type inequalities for LR-$ p $-convex interval-valued functions (LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>) are constructed in this study. Second, for the product of p-convex various Hermite-Hadamard (<italic>HH</italic>) type integral inequalities are established. Similarly, we also obtain Hermite-Hadamard-Fejér (<italic>HH</italic>-Fejér) type integral inequality for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>. Finally, for LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic>, various discrete Schur's and Jensen's type inequalities are presented. Moreover, the results presented in this study are verified by useful nontrivial examples. Some of the results reported here for be LR-$ p $-convex-<italic>I</italic>-<italic>V</italic>-<italic>F</italic> are generalizations of prior results for convex and harmonically convex functions, as well as $ p $-convex functions.</p> </abstract>

On inequalities of Hermite-Hadamard type via $ n $-polynomial exponential type $ s $-convex functions

<abstract><p>In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as $ n $-polynomial exponential type $ s $-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications.</p></abstract>

Hermite-Hadamard type integral inequalities for the class of strongly convex functions on time scales

Hermite-Hadamard type integral inequalities for the class of strongly convex functions on time scales

Novel Analysis of Hermite–Hadamard Type Integral Inequalities via Generalized Exponential Type m-Convex Functions

The theory of convexity has a rich and paramount history and has been the interest of intense research for longer than a century in mathematics. It has not just fascinating and profound outcomes in different branches of engineering and mathematical sciences, it also has plenty of uses because of its geometrical interpretation and definition. It also provides numerical quadrature rules and tools for researchers to tackle and solve a wide class of related and unrelated problems. The main focus of this paper is to introduce and explore the concept of a new family of convex functions namely generalized exponential type m-convex functions. Further, to upgrade its numerical significance, we present some of its algebraic properties. Using the newly introduced definition, we investigate the novel version of Hermite–Hadamard type integral inequality. Furthermore, we establish some integral identities, and employing these identities, we present several new Hermite–Hadamard H–H type integral inequalities for generalized exponential type m-convex functions. These new results yield some generalizations of the prior results in the literature.

A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions

The main objective of this article is to employ the concept of preinvexity to establish some new inequalities. In addition, we discuss some algebraic properties and examples of the generalized preinvex function. With the help of this new relation, we present new version of Hermite-Hadamard inequality and its some of its refinements using fundamental inequalities like Hölder, power-mean, Hölder-Iscan, and improved power-mean inequality. These results are speculations of various recently known outcomes. The immeasurable concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field.

Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.