{"title":"通过量子微积分实现强$$(\\alpha ,m)$$凸函数的赫米特-哈达马德式不等式","authors":"Shashi Kant Mishra, Ravina Sharma, Jaya Bisht","doi":"10.1007/s12190-024-02135-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we derive a quantum analogue of Hermite–Hadamard-type inequalities for twice differentiable convex functions whose second derivatives in absolute value are strongly <span>\\((\\alpha ,m )\\)</span>-convex. We obtain new bounds using the H<span>\\(\\ddot{o}\\)</span>lder and power mean inequalities. Moreover, we provide suitable examples in support of our theoretical results. We correlate our findings with comparable results in the literature and show that the obtained results are refinements and improvements.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"33 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hermite–Hadamard-type inequalities for strongly $$(\\\\alpha ,m)$$ -convex functions via quantum calculus\",\"authors\":\"Shashi Kant Mishra, Ravina Sharma, Jaya Bisht\",\"doi\":\"10.1007/s12190-024-02135-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we derive a quantum analogue of Hermite–Hadamard-type inequalities for twice differentiable convex functions whose second derivatives in absolute value are strongly <span>\\\\((\\\\alpha ,m )\\\\)</span>-convex. We obtain new bounds using the H<span>\\\\(\\\\ddot{o}\\\\)</span>lder and power mean inequalities. Moreover, we provide suitable examples in support of our theoretical results. We correlate our findings with comparable results in the literature and show that the obtained results are refinements and improvements.</p>\",\"PeriodicalId\":15034,\"journal\":{\"name\":\"Journal of Applied Mathematics and Computing\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics and Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12190-024-02135-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02135-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hermite–Hadamard-type inequalities for strongly $$(\alpha ,m)$$ -convex functions via quantum calculus
In this paper, we derive a quantum analogue of Hermite–Hadamard-type inequalities for twice differentiable convex functions whose second derivatives in absolute value are strongly \((\alpha ,m )\)-convex. We obtain new bounds using the H\(\ddot{o}\)lder and power mean inequalities. Moreover, we provide suitable examples in support of our theoretical results. We correlate our findings with comparable results in the literature and show that the obtained results are refinements and improvements.
期刊介绍:
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.