Some Integral Inequalities for &lt;em&gt;h&lt;/em&gt;-Godunova-Levin Preinvexity

Almutairi, Ohud; Kılıçman, Adem

doi:10.20944/preprints201911.0196.v1

2019

DOI: 10.20944/preprints201911.0196.v1

|View full text |Cite

Preprint

Some Integral Inequalities for <em>h</em>-Godunova-Levin Preinvexity

Ohud Almutairi¹,

Adem Kılıçman²

Abstract: In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

Help me understand this report

View published versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2024

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

References 14 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Some New Integral Inequalities for Generalized Preinvex Functions in Interval-Valued Settings

Khan

Macías‐Díaz

Soliman

et al. 2022

Axioms

View full text Add to dashboard Cite

In recent years, there has been a significant amount of research on the extension of convex functions which are known as preinvex functions. In this paper, we have used this approach to generalize the preinvex interval-valued function in terms of (£1,£2)-preinvex interval-valued functions because of its extraordinary applications in both pure and applied mathematics. The idea of (£1,£2) -preinvex interval-valued functions is explained in this work. By using the Riemann integral operator, we obtain Hermite-Hadamard and Fejér-type inequalities for (£1,£2) -preinvex interval-valued functions. To discuss the validity of our main results, we provide non-trivial examples. Some exceptional cases have been discussed that can be seen as applications of main outcomes.

show abstract

Some New Integral Inequalities for Generalized Preinvex Functions in Interval-Valued Settings

Khan

Macías‐Díaz

Soliman

et al. 2022

Axioms

View full text Add to dashboard Cite

show abstract

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Cortez,

Althobaiti,

Aljohani

et al. 2024

Axioms

View full text Add to dashboard Cite

Convex inequalities and fuzzy-valued calculus converge to form a comprehensive mathematical framework that can be employed to understand and analyze a broad spectrum of issues. This paper utilizes fuzzy Aumman’s integrals to establish integral inequalities of Hermite-Hahadard, Fejér, and Pachpatte types within up and down (U·D) relations and over newly defined class U·D-ħ-Godunova–Levin convex fuzzy-number mappings. To demonstrate the unique properties of U·D-relations, recent findings have been developed using fuzzy Aumman’s, as well as various other fuzzy partial order relations that have notable deficiencies outlined in the literature. Several compelling examples were constructed to validate the derived results, and multiple notes were provided to illustrate, depending on the configuration, that this type of integral operator generalizes several previously documented conclusions. This endeavor can potentially advance mathematical theory, computational techniques, and applications across various fields.

show abstract

Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation

et al. 2023

View full text Add to dashboard Cite

Convex bodies are naturally symmetrical. There is also a correlation between the two variables of symmetry and convexity. Their use, in either case, has been feasible in recent years because of their interchangeable and similar properties. The proposed analysis provides information on a new class for a convex function which is known as up and down X1,X2-convex fuzzy-Number valued mappings (UD-X1,X2-convex FNVM). Using this class, we disclosed a number of new versions of integral inequalities. Additionally, we give a number of new related integral inequalities connected to the well-known Hermite-Hadamard-type inequalities. In conclusion, some examples are given to back up and show the value of these new results.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Some Integral Inequalities for <em>h</em>-Godunova-Levin Preinvexity

Cited by 5 publications

References 14 publications

Some New Integral Inequalities for Generalized Preinvex Functions in Interval-Valued Settings

Some New Integral Inequalities for Generalized Preinvex Functions in Interval-Valued Settings

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation

Contact Info

Product

Resources

About