Open AccessNEW MULTI-FUNCTIONAL APPROACH FOR κTH-ORDER DIFFERENTIABILITY GOVERNED BY FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ℏ)-CONVEX FUNCTIONS IN HILBERT SPACE
Author(s) -
Miao-Kun Wang,
Saima Rashid,
Yeliz Karaca,
Dumitru Băleanu,
YuMing Chu
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x21400193
Subject(s) - quasiconvex function , mathematics , convex function , pure mathematics , operator (biology) , fractional calculus , effective domain , subderivative , regular polygon , hilbert space , function (biology) , order (exchange) , lipschitz continuity , differentiable function , mathematical analysis , convex optimization , biochemistry , chemistry , geometry , finance , repressor , evolutionary biology , biology , transcription factor , economics , gene
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized [Formula: see text]-convex and approximately [Formula: see text]-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 [Formula: see text]-convex functions such as higher-order strongly (HOS) generalized [Formula: see text]-convex functions and HOS generalized [Formula: see text]-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 [Formula: see text]-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized [Formula: see text]-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.