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 𝔴-preinvex interval-valued function using an interval integral operator. In...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/9/1901 |
| _version_ | 1797481952306003968 |
|---|---|
| author | Muhammad Bilal Khan Savin Treanțǎ Mohamed S. Soliman |
| author_facet | Muhammad Bilal Khan Savin Treanțǎ Mohamed S. Soliman |
| author_sort | Muhammad Bilal Khan |
| collection | DOAJ |
| description | 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 𝔴-preinvex interval-valued function using an interval integral operator. In the context of pseudo-order relations, we also establish new variations of the Fejér type inequalities and the Pachpatte type inequalities. We further verify the veracity of the conclusions we draw in this study by providing a number of numerical examples. The findings given in this work, in our opinion, are innovative and will help spur more study in this area. |
| first_indexed | 2024-03-09T22:22:40Z |
| format | Article |
| id | doaj.art-ea1976745b764e99b5b6633948446d4f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:22:40Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ea1976745b764e99b5b6633948446d4f2023-11-23T19:12:50ZengMDPI AGSymmetry2073-89942022-09-01149190110.3390/sym14091901Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type InequalitiesMuhammad Bilal Khan0Savin Treanțǎ1Mohamed S. Soliman2Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThis 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 𝔴-preinvex interval-valued function using an interval integral operator. In the context of pseudo-order relations, we also establish new variations of the Fejér type inequalities and the Pachpatte type inequalities. We further verify the veracity of the conclusions we draw in this study by providing a number of numerical examples. The findings given in this work, in our opinion, are innovative and will help spur more study in this area.https://www.mdpi.com/2073-8994/14/9/1901Hermite–Hadamard inequalitiesinterval-valued functionsRiemann integral operator |
| spellingShingle | Muhammad Bilal Khan Savin Treanțǎ Mohamed S. Soliman Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities Symmetry Hermite–Hadamard inequalities interval-valued functions Riemann integral operator |
| title | Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities |
| title_full | Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities |
| title_fullStr | Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities |
| title_full_unstemmed | Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities |
| title_short | Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities |
| title_sort | generalized preinvex interval valued functions and related hermite hadamard type inequalities |
| topic | Hermite–Hadamard inequalities interval-valued functions Riemann integral operator |
| url | https://www.mdpi.com/2073-8994/14/9/1901 |
| work_keys_str_mv | AT muhammadbilalkhan generalizedpreinvexintervalvaluedfunctionsandrelatedhermitehadamardtypeinequalities AT savintreanta generalizedpreinvexintervalvaluedfunctionsandrelatedhermitehadamardtypeinequalities AT mohamedssoliman generalizedpreinvexintervalvaluedfunctionsandrelatedhermitehadamardtypeinequalities |