Generalized n -Polynomial p -Convexity and Related Inequalities

Serap Özcan and Luminiţa-Ioana Cotîrlă ()
Additional contact information
Serap Özcan: Department of Mathematics, Faculty of Arts and Sciences, Kırklareli University, 39100 Kırklareli, Turkey
Luminiţa-Ioana Cotîrlă: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 7, 1-15

Abstract: In this paper, we construct a new class of convex functions, so-called generalized n -polynomial p -convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n -polynomial p -convex. When p = − 1 , our definition evolves into a new definition for the class of convex functions so-called generalized n -polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.

Keywords: convex function; n-polynomial convexity; generalized n-polynomial p-convexity; Hermite–Hadamard inequality; integral inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/7/1042/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/7/1042/ (text/html)

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:gam:jmathe:v:12:y:2024:i:7:p:1042-:d:1367628

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().