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Search Results (3)

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Keywords = harmonically cr-h-convex

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21 pages, 420 KB  
Article
Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr-h-Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings
by Yahya Almalki and Waqar Afzal
Mathematics 2023, 11(19), 4041; https://doi.org/10.3390/math11194041 - 23 Sep 2023
Cited by 14 | Viewed by 1354
Abstract
The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville) and generalize [...] Read more.
The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h-convex functions. First, using these notions, we developed the Hermite–Hadamard (H–H) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples. Full article
(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)
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16 pages, 362 KB  
Article
Some New Generalizations of Integral Inequalities for Harmonical cr-(h1,h2)-Godunova–Levin Functions and Applications
by Tareq Saeed, Waqar Afzal, Mujahid Abbas, Savin Treanţă and Manuel De la Sen
Mathematics 2022, 10(23), 4540; https://doi.org/10.3390/math10234540 - 1 Dec 2022
Cited by 22 | Viewed by 2144
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)
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15 pages, 309 KB  
Article
The Properties of Harmonically cr-h-Convex Function and Its Applications
by Wei Liu, Fangfang Shi, Guoju Ye and Dafang Zhao
Mathematics 2022, 10(12), 2089; https://doi.org/10.3390/math10122089 - 16 Jun 2022
Cited by 28 | Viewed by 2268
Abstract
In this paper, the definition of the harmonically cr-h-convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically cr-h-convex functions are also established. [...] Read more.
In this paper, the definition of the harmonically cr-h-convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically cr-h-convex functions are also established. In addition, some numerical examples are given to verify the accuracy of the results. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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