{"title":"关于多元回归计算中的多元(s,P)相等性及相关的分数不等式","authors":"YU PENG, TINGSONG DU","doi":"10.1142/s0218348x24500488","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we propose a fresh conception about convexity, known as the multiplicative <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>differentiable <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS\",\"authors\":\"YU PENG, TINGSONG DU\",\"doi\":\"10.1142/s0218348x24500488\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we propose a fresh conception about convexity, known as the multiplicative <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mo stretchy=\\\"false\\\">(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo stretchy=\\\"false\\\">)</mo></math></span><span></span>-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><msup><mrow></mrow><mrow><mo stretchy=\\\"false\\\">∗</mo></mrow></msup></math></span><span></span>differentiable <span><math altimg=\\\"eq-00005.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mo stretchy=\\\"false\\\">(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo stretchy=\\\"false\\\">)</mo></math></span><span></span>-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.</p>\",\"PeriodicalId\":501262,\"journal\":{\"name\":\"Fractals\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractals\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x24500488\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x24500488","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS
In this paper, we propose a fresh conception about convexity, known as the multiplicative -convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the differentiable -convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.