Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications
Many researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the subject over the years. An essential part of the th...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/2/278 |
| _version_ | 1797439043641802752 |
|---|---|
| author | Asfand Fahad Ayesha Yuanheng Wang Saad Ihsaan Butt |
| author_facet | Asfand Fahad Ayesha Yuanheng Wang Saad Ihsaan Butt |
| author_sort | Asfand Fahad |
| collection | DOAJ |
| description | Many researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the subject over the years. An essential part of the theory of mathematical inequalities is the convex function and its extensions. In the recent past, the study of Jensen–Mercer inequality and Hermite–Hadamard–Mercer type inequalities has remained a topic of interest in mathematical inequalities. In this paper, we study several inequalities for GA-<i>h</i>-convex functions and its subclasses, including GA-convex functions, GA-<i>s</i>-convex functions, GA-<i>Q</i>-convex functions, and GA-<i>P</i>-convex functions. We prove the Jensen–Mercer inequality for GA-<i>h</i>-convex functions and give weighted Hermite–Hadamard inequalities by applying the newly established Jensen–Mercer inequality. We also establish inequalities of Hermite–Hadamard–Mercer type. Thus, we give new insights and variants of Jensen–Mercer and related inequalities for GA-<i>h</i>-convex functions. Furthermore, we apply our main results along with Hadamard fractional integrals to prove weighted Hermite–Hadamard–Mercer inequalities for GA-<i>h</i>-convex functions and its subclasses. As special cases of the proven results, we capture several well-known results from the relevant literature. |
| first_indexed | 2024-03-09T11:47:07Z |
| format | Article |
| id | doaj.art-0b1446ba21dd457b86cb783f07efdc7e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:47:07Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0b1446ba21dd457b86cb783f07efdc7e2023-11-30T23:19:57ZengMDPI AGMathematics2227-73902023-01-0111227810.3390/math11020278Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with ApplicationsAsfand Fahad0Ayesha1Yuanheng Wang2Saad Ihsaan Butt3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Vehari Campus, COMSATS University Islamabad, Vehari 61100, PakistanDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Lahore Campus, COMSATS University Islamabad, Lahore 54000, PakistanMany researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the subject over the years. An essential part of the theory of mathematical inequalities is the convex function and its extensions. In the recent past, the study of Jensen–Mercer inequality and Hermite–Hadamard–Mercer type inequalities has remained a topic of interest in mathematical inequalities. In this paper, we study several inequalities for GA-<i>h</i>-convex functions and its subclasses, including GA-convex functions, GA-<i>s</i>-convex functions, GA-<i>Q</i>-convex functions, and GA-<i>P</i>-convex functions. We prove the Jensen–Mercer inequality for GA-<i>h</i>-convex functions and give weighted Hermite–Hadamard inequalities by applying the newly established Jensen–Mercer inequality. We also establish inequalities of Hermite–Hadamard–Mercer type. Thus, we give new insights and variants of Jensen–Mercer and related inequalities for GA-<i>h</i>-convex functions. Furthermore, we apply our main results along with Hadamard fractional integrals to prove weighted Hermite–Hadamard–Mercer inequalities for GA-<i>h</i>-convex functions and its subclasses. As special cases of the proven results, we capture several well-known results from the relevant literature.https://www.mdpi.com/2227-7390/11/2/278convex functions<i>h</i>-convex functionsGA-<i>h</i>-convex functionsJensen–Mercer inequalityHermite–Hadamard–Mercer type inequalitiesHadamard fractional integral |
| spellingShingle | Asfand Fahad Ayesha Yuanheng Wang Saad Ihsaan Butt Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications Mathematics convex functions <i>h</i>-convex functions GA-<i>h</i>-convex functions Jensen–Mercer inequality Hermite–Hadamard–Mercer type inequalities Hadamard fractional integral |
| title | Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications |
| title_full | Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications |
| title_fullStr | Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications |
| title_full_unstemmed | Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications |
| title_short | Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-<i>h</i>-Convex Functions and Its Subclasses with Applications |
| title_sort | jensen mercer and hermite hadamard mercer type inequalities for ga i h i convex functions and its subclasses with applications |
| topic | convex functions <i>h</i>-convex functions GA-<i>h</i>-convex functions Jensen–Mercer inequality Hermite–Hadamard–Mercer type inequalities Hadamard fractional integral |
| url | https://www.mdpi.com/2227-7390/11/2/278 |
| work_keys_str_mv | AT asfandfahad jensenmercerandhermitehadamardmercertypeinequalitiesforgaihiconvexfunctionsanditssubclasseswithapplications AT ayesha jensenmercerandhermitehadamardmercertypeinequalitiesforgaihiconvexfunctionsanditssubclasseswithapplications AT yuanhengwang jensenmercerandhermitehadamardmercertypeinequalitiesforgaihiconvexfunctionsanditssubclasseswithapplications AT saadihsaanbutt jensenmercerandhermitehadamardmercertypeinequalitiesforgaihiconvexfunctionsanditssubclasseswithapplications |