{"title":"通过 FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL 测量ℏ-反函数的 HERMITE-HADAMARD 类型不等式","authors":"HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA","doi":"10.1142/s0218348x24500427","DOIUrl":null,"url":null,"abstract":"<p>Fractional <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-calculus is considered to be the fractional analogs of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℏ</mi></math></span><span></span>-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span>-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.</p>","PeriodicalId":501262,"journal":{"name":"Fractals","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL\",\"authors\":\"HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA\",\"doi\":\"10.1142/s0218348x24500427\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Fractional <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>q</mi></math></span><span></span>-calculus is considered to be the fractional analogs of <span><math altimg=\\\"eq-00005.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>q</mi></math></span><span></span>-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) <span><math altimg=\\\"eq-00006.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>q</mi></math></span><span></span>-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving <span><math altimg=\\\"eq-00007.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>ℏ</mi></math></span><span></span>-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF <span><math altimg=\\\"eq-00008.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>q</mi></math></span><span></span>-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.</p>\",\"PeriodicalId\":501262,\"journal\":{\"name\":\"Fractals\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-05\",\"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/s0218348x24500427\",\"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/s0218348x24500427","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL
Fractional -calculus is considered to be the fractional analogs of -calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) -integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving -convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF -integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.
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