Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Zareen A. Khan; Waqar Afzal; Mujahid Abbas; Kwara Nantomah

doi:10.1155/jom/5570638

Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Zareen A. Khan
, Waqar Afzal
, Mujahid Abbas
, Kwara Nantomah

Construction Management and Quantity Surveying

Princess Nourah Bint Abdulrahman University
University of Gujrat
Government College University Lahore
China Medical University Taichung
C. K. Tedam University of Technology and Applied Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this note, we introduce the concept of ℏ-Godunova–Levin interval-valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér-type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.

Original language	English
Article number	5570638
Journal	Journal of Mathematics
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1155/jom/5570638
Publication status	Published - 2025

Keywords

Fejér
Godunova–Levin
Hermite–Hadamard
interval maps
preinvex

ASJC Scopus subject areas

General Mathematics

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10.1155/jom/5570638

Cite this

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title = "Some Novel Inequalities for Godunova{\textendash}Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation",

abstract = "In this note, we introduce the concept of ℏ-Godunova{\textendash}Levin interval-valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite{\textendash}Hadamard and Fej{\'e}r-type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.",

keywords = "Fej{\'e}r, Godunova{\textendash}Levin, Hermite{\textendash}Hadamard, interval maps, preinvex",

author = "Khan, \{Zareen A.\} and Waqar Afzal and Mujahid Abbas and Kwara Nantomah",

note = "Publisher Copyright: Copyright {\textcopyright} 2025 Zareen A. Khan et al. Journal of Mathematics published by John Wiley \& Sons Ltd.",

year = "2025",

doi = "10.1155/jom/5570638",

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AU - Khan, Zareen A.

AU - Afzal, Waqar

AU - Abbas, Mujahid

AU - Nantomah, Kwara

PY - 2025

Y1 - 2025

N2 - In this note, we introduce the concept of ℏ-Godunova–Levin interval-valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér-type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.

AB - In this note, we introduce the concept of ℏ-Godunova–Levin interval-valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér-type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.

KW - Fejér

KW - Godunova–Levin

KW - Hermite–Hadamard

KW - interval maps

KW - preinvex

UR - https://www.scopus.com/pages/publications/105001592888

U2 - 10.1155/jom/5570638

DO - 10.1155/jom/5570638

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AN - SCOPUS:105001592888

SN - 2314-4629

VL - 2025

JO - Journal of Mathematics

JF - Journal of Mathematics

IS - 1

M1 - 5570638

ER -

Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Abstract

Keywords

ASJC Scopus subject areas

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