Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-h-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...
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| Veröffentlicht in: | Mathematics (Basel) Jg. 11; H. 2; S. 278 |
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| Abstract | 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-h-convex functions and its subclasses, including GA-convex functions, GA-s-convex functions, GA-Q-convex functions, and GA-P-convex functions. We prove the Jensen–Mercer inequality for GA-h-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-h-convex functions. Furthermore, we apply our main results along with Hadamard fractional integrals to prove weighted Hermite–Hadamard–Mercer inequalities for GA-h-convex functions and its subclasses. As special cases of the proven results, we capture several well-known results from the relevant literature. |
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| AbstractList | 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-h-convex functions and its subclasses, including GA-convex functions, GA-s-convex functions, GA-Q-convex functions, and GA-P-convex functions. We prove the Jensen–Mercer inequality for GA-h-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-h-convex functions. Furthermore, we apply our main results along with Hadamard fractional integrals to prove weighted Hermite–Hadamard–Mercer inequalities for GA-h-convex functions and its subclasses. As special cases of the proven results, we capture several well-known results from the relevant literature. |
| Author | Fahad, Asfand Butt, Saad Ihsaan Ayesha Wang, Yuanheng |
| Author_xml | – sequence: 1 givenname: Asfand surname: Fahad fullname: Fahad, Asfand – sequence: 2 surname: Ayesha fullname: Ayesha – sequence: 3 givenname: Yuanheng orcidid: 0000-0003-4079-2850 surname: Wang fullname: Wang, Yuanheng – sequence: 4 givenname: Saad Ihsaan orcidid: 0000-0001-7192-8269 surname: Butt fullname: Butt, Saad Ihsaan |
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| Cites_doi | 10.1186/s13660-020-02478-7 10.1016/j.amc.2014.12.018 10.1016/j.aej.2022.10.019 10.1016/j.amc.2015.06.051 10.1016/j.jmaa.2006.02.086 10.7153/mia-06-53 10.3934/math.2020412 10.1090/S0002-9904-1948-08994-7 10.1016/j.amc.2007.03.030 10.2298/FIL1806193L 10.1016/j.cam.2021.114049 10.1016/j.cie.2020.106634 10.3390/fractalfract5040269 10.1016/j.chaos.2019.109547 10.1016/j.aej.2021.10.033 10.1016/j.chaos.2020.110554 10.1016/j.chaos.2021.111025 10.1186/1029-242X-2013-491 10.1186/s13660-021-02735-3 10.3390/sym14020294 |
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| SubjectTerms | Convex analysis convex functions Fractional calculus GA-h-convex functions h-convex functions Hadamard fractional integral Hermite–Hadamard–Mercer type inequalities Inequalities Inequality Integrals Jensen–Mercer inequality Mathematical analysis Mathematical functions Optimization Trends |
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