NEW MULTI-FUNCTIONAL APPROACH FOR κTH-ORDER DIFFERENTIABILITY GOVERNED BY FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ℠)-CONVEX FUNCTIONS IN HILBERT SPACE

Miao-Kun Wang (), Saima Rashid (), Yeliz Karaca (), Dumitru Baleanu () and Yu-Ming Chu
Additional contact information
Miao-Kun Wang: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Yeliz Karaca: University of Massachusetts Medical School, Worcester, MA 01655, USA
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara, Turkey
Yu-Ming Chu: College of Science, Hunan City University, Yiyang 413000, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-23

Abstract: This 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.

Keywords: Convex Functions; Generalized (ψ; ℠)-Convex Functions; κ-th Order Differentiability; Raina’s Function; Breckner-Type Function; Godunova–Levin-Type Function (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X21400193
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21400193

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X21400193

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().