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Some integral inequalities for generalized preinvex functions with applications
- Source :
- AIMS Mathematics, Vol 6, Iss 12, Pp 13907-13930 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- The main objective of this work is to explore and characterize the idea of $ s $-type preinvex function and related inequalities. Some interesting algebraic properties and logical examples are given to support the newly introduced idea. In addition, we attain the novel version of Hermite-Hadamard type inequality utilizing the introduced preinvexity. Furthermore, we establish two new identities, and employing these, we present some refinements of Hermite-Hadamard-type inequality. Some special cases of the presented results for different preinvex functions are deduced as well. Finally, as applications, some new inequalities for the arithmetic, geometric and harmonic means are established. Results obtained in this paper can be viewed as a significant improvement of previously known results. The awe-inspiring concepts and formidable tools of this paper may invigorate and revitalize for additional research in this worthy and absorbing field.
- Subjects :
- Algebraic properties
s-type preinvexity
Inequality
Computer science
General Mathematics
media_common.quotation_subject
Harmonic mean
Field (mathematics)
Function (mathematics)
Type inequality
hölder-i̇şcan inequality
Additional research
Algebra
improved power-mean integral inequality
QA1-939
Mathematics
media_common
preinvex function
hölder's inequality
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 12
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....52d674c321c23881e27654cfe0faa3cb