{"title":"分形(m,h)-预倒凸映射的性质和2α α -分形加权参数不等式","authors":"XIAOHUA ZHANG, YUNXIU ZHOU, TINGSONG DU","doi":"10.1142/s0218348x23501347","DOIUrl":null,"url":null,"abstract":"The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS\",\"authors\":\"XIAOHUA ZHANG, YUNXIU ZHOU, TINGSONG DU\",\"doi\":\"10.1142/s0218348x23501347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2023-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x23501347\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x23501347","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS
The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.
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