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 a...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/9/1774 |
| _version_ | 1797482075832451072 |
|---|---|
| author | Muhammad Amer Latif Humaira Kalsoom Muhammad Zainul Abidin |
| author_facet | Muhammad Amer Latif Humaira Kalsoom Muhammad Zainul Abidin |
| author_sort | Muhammad Amer Latif |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T22:23:07Z |
| format | Article |
| id | doaj.art-69382843393d4a5bbfe1e02a82467b02 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:23:07Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-69382843393d4a5bbfe1e02a82467b022023-11-23T19:10:44ZengMDPI AGSymmetry2073-89942022-08-01149177410.3390/sym14091774Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral OperatorMuhammad Amer Latif0Humaira Kalsoom1Muhammad Zainul Abidin2Department of Basic Sciences, King Faisal University, Hofuf 31982, Saudi ArabiaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaFractional 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.https://www.mdpi.com/2073-8994/14/9/1774harmonic convex functionsHermite–Hadamard-type inequalitiesAtangana–Baleanu fractional integral operatorpower-mean inequalityHölder inequality |
| spellingShingle | Muhammad Amer Latif Humaira Kalsoom Muhammad Zainul Abidin Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator Symmetry harmonic convex functions Hermite–Hadamard-type inequalities Atangana–Baleanu fractional integral operator power-mean inequality Hölder inequality |
| title | Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator |
| title_full | Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator |
| title_fullStr | Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator |
| title_full_unstemmed | Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator |
| title_short | Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator |
| title_sort | hermite hadamard type inequalities involving harmonically convex function via the atangana baleanu fractional integral operator |
| topic | harmonic convex functions Hermite–Hadamard-type inequalities Atangana–Baleanu fractional integral operator power-mean inequality Hölder inequality |
| url | https://www.mdpi.com/2073-8994/14/9/1774 |
| work_keys_str_mv | AT muhammadamerlatif hermitehadamardtypeinequalitiesinvolvingharmonicallyconvexfunctionviatheatanganabaleanufractionalintegraloperator AT humairakalsoom hermitehadamardtypeinequalitiesinvolvingharmonicallyconvexfunctionviatheatanganabaleanufractionalintegraloperator AT muhammadzainulabidin hermitehadamardtypeinequalitiesinvolvingharmonicallyconvexfunctionviatheatanganabaleanufractionalintegraloperator |