{"title":"Differentiability of Functions on Spheres and Criterions of Convexity","authors":"Tingting Chen, Qi Guo","doi":"10.1051/wujns/2022274273","DOIUrl":null,"url":null,"abstract":"Some basic concepts for functions defined on subsets of the unit sphere, such as the s-directional derivative, s-gradient and s-Gateaux and s-Frechet differentiability etc, are introduced and investigated. These concepts are different from the usual ones for functions defined on subsets of Euclidean spaces, however, the results obtained here are very similar. Then, as applications, we provide some criterions of s-convexity for functions defined on unit spheres which are improvements or refinements of some known results.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wuhan University Journal of Natural Sciences","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.1051/wujns/2022274273","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
引用次数: 0
Abstract
Some basic concepts for functions defined on subsets of the unit sphere, such as the s-directional derivative, s-gradient and s-Gateaux and s-Frechet differentiability etc, are introduced and investigated. These concepts are different from the usual ones for functions defined on subsets of Euclidean spaces, however, the results obtained here are very similar. Then, as applications, we provide some criterions of s-convexity for functions defined on unit spheres which are improvements or refinements of some known results.
期刊介绍:
Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.