Generalized Hermite-Hadamard-Mercer type inequalities via majorization

Faisal, Shah; Khan, Muhammad Adil; Iqbal, Sajid

doi:10.2298/fil2202469f

Cited by 19 publications

(6 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Inequalities are one of the important topics of mathematics, and in this field, convex functions and their generalizations play an important role. In [26][27][28], the authors focused on Hermite-Hadamard inequalities by using the majorization and some properties of convex functions. Later, some other researchers combined these notions with monocity and boundedness [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

Kara

Budak

Etemad

et al. 2023

Journal of Function Spaces

View full text Add to dashboard Cite

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder’s inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.

show abstract

Section: Introductionmentioning

confidence: 99%

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

Kara

Budak

Etemad

et al. 2023

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…Utilizing a number of fundamental integral inequalities, we explore how convexity might be encouraged subjectively. It has been reported recently that convex functions have been rigorously generalized, see [11][12][13][14]. There have recently been studies that extend some of these inequalities to functions with interval values, see [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation

et al. 2022

View full text Add to dashboard Cite

There are different types of order relations that are associated with interval analysis for determining integral inequalities. The purpose of this paper is to connect the inequalities terms to total order relations, often called (CR)-order. In contrast to classical interval-order relations, total order relations are quite different and novel in the literature and are calculated as ω=⟨ωc,ωr⟩=⟨ω¯+ω̲2,ω¯−ω̲2⟩. A major benefit of total order relations is that they produce more efficient results than other order relations. This study introduces the notion of CR-(h1,h2)-convex function using total order relations. Center and Radius order relations are a powerful tool for studying inequalities based on their properties and widespread application. Using this novel notion, we first developed some variants of Hermite–Hadamard inequality and then constructed Jensen inequality. Based on the results, this new concept is extremely useful in connection with a variety of inequalities. There are many new and well-known convex functions unified by this type of convexity. These results will stimulate further research on inequalities for fractional interval-valued functions and fuzzy interval-valued functions, as well as the optimization problems associated with them. For the purpose of verifying our main findings, we provide some nontrivial examples.

show abstract

“…Different convex functions have been used by several authors to expand and generalize integral inequalities; see Refs. [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Some New Generalizations of Integral Inequalities for Harmonical cr-(h1,h2)-Godunova–Levin Functions and Applications

et al. 2022

View full text Add to dashboard Cite

The interval analysis is famous for its ability to deal with uncertain data. This method is useful for addressing models with data that contain inaccuracies. Different concepts are used to handle data uncertainty in an interval analysis, including a pseudo-order relation, inclusion relation, and center–radius (cr)-order relation. This study aims to establish a connection between inequalities and a cr-order relation. In this article, we developed the Hermite–Hadamard (H.H) and Jensen-type inequalities using the notion of harmonical (h1,h2)-Godunova–Levin (GL) functions via a cr-order relation which is very novel in the literature. These new definitions have allowed us to identify many classical and novel special cases that illustrate our main findings. It is possible to unify a large number of well-known convex functions using the principle of this type of convexity. Furthermore, for the sake of checking the validity of our main findings, some nontrivial examples are given.

show abstract

Generalized Hermite-Hadamard-Mercer type inequalities via majorization

Cited by 19 publications

References 32 publications

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation

Some New Generalizations of Integral Inequalities for Harmonical cr-(h1,h2)-Godunova–Levin Functions and Applications

Contact Info

Product

Resources

About