{"title":"一些涉及扩展伽玛函数和Kummer合流超几何k-函数的不等式。","authors":"Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, Muhammad Arshad","doi":"10.1186/s13660-018-1717-8","DOIUrl":null,"url":null,"abstract":"<p><p>In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric <i>k</i>-function via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent <i>k</i>-hypergeometric function.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1717-8","citationCount":"41","resultStr":"{\"title\":\"Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric <i>k</i>-function.\",\"authors\":\"Kottakkaran Sooppy Nisar, Feng Qi, Gauhar Rahman, Shahid Mubeen, Muhammad Arshad\",\"doi\":\"10.1186/s13660-018-1717-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric <i>k</i>-function via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent <i>k</i>-hypergeometric function.</p>\",\"PeriodicalId\":49163,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13660-018-1717-8\",\"citationCount\":\"41\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-018-1717-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/6/19 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1717-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/6/19 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function.
In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function.
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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