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NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE

dc.contributor.authorWang, Miao-Kun
dc.contributor.authorRashid, Saima
dc.contributor.authorKaraca, Yeliz
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorChu, Yu-Ming
dc.contributor.authorID56389tr_TR
dc.date.accessioned2022-07-07T11:46:11Z
dc.date.available2022-07-07T11:46:11Z
dc.date.issued2021
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractThis work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (ψ, ?)-convex functions such as higher-order strongly (HOS) generalized (ψ, ?)-convex functions and HOS generalized ψ-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (ψ, ?)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized ψ-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields. © 2021 The Author(s).en_US
dc.description.publishedMonth8
dc.identifier.citationWang, Miao-Kun...et al. (2021). "NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE", Fractals, Vol. 29, No. 5.en_US
dc.identifier.doi10.1142/S0218348X21400193
dc.identifier.issn0218-348X
dc.identifier.issue5en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/5725
dc.identifier.volume29en_US
dc.language.isoenen_US
dc.relation.ispartofFractalsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBreckner-Type Functionen_US
dc.subjectConvex Functionsen_US
dc.subjectGeneralized (ψ, ?) -Convex Functionsen_US
dc.subjectGodunova-Levin-Type Functionen_US
dc.subjectRaina's Functionen_US
dc.subjectκ -th Order Differentiabilityen_US
dc.titleNEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACEtr_TR
dc.titleNew Multi-Functional Approach for Κ Th-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, ?) -Convex Functions in Hilbert Spaceen_US
dc.typeArticleen_US
dspace.entity.typePublication

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