Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications
The main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional...
Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2493944 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565821699784704 |
|---|---|
| author | Artion Kashuri Soubhagya Kumar Sahoo Bibhakar Kodamasingh Muhammad Tariq Ahmed A. Hamoud Homan Emadifar Faraidun K. Hamasalh Nedal M. Mohammed Masoumeh Khademi |
| author_facet | Artion Kashuri Soubhagya Kumar Sahoo Bibhakar Kodamasingh Muhammad Tariq Ahmed A. Hamoud Homan Emadifar Faraidun K. Hamasalh Nedal M. Mohammed Masoumeh Khademi |
| author_sort | Artion Kashuri |
| collection | DOAJ |
| description | The main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues. Further, we prove two interesting integral and fractional identities for differentiable mappings, and, using them as auxiliary results, some refinements of Hermite–Hadamard type integral inequalities for both classical and fractional versions are presented. Finally, in order to show the efficiency of our results, some applications for special means and error estimations are obtained as well. |
| format | Article |
| id | doaj-art-e03b46f549de4c1584bfa3d5b1f9616e |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e03b46f549de4c1584bfa3d5b1f9616e2025-02-03T01:06:37ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2493944Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their ApplicationsArtion Kashuri0Soubhagya Kumar Sahoo1Bibhakar Kodamasingh2Muhammad Tariq3Ahmed A. Hamoud4Homan Emadifar5Faraidun K. Hamasalh6Nedal M. Mohammed7Masoumeh Khademi8Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Basic Sciences and Related StudiesDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics & Computer ScienceDepartment of MathematicsThe main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues. Further, we prove two interesting integral and fractional identities for differentiable mappings, and, using them as auxiliary results, some refinements of Hermite–Hadamard type integral inequalities for both classical and fractional versions are presented. Finally, in order to show the efficiency of our results, some applications for special means and error estimations are obtained as well.http://dx.doi.org/10.1155/2022/2493944 |
| spellingShingle | Artion Kashuri Soubhagya Kumar Sahoo Bibhakar Kodamasingh Muhammad Tariq Ahmed A. Hamoud Homan Emadifar Faraidun K. Hamasalh Nedal M. Mohammed Masoumeh Khademi Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications Journal of Mathematics |
| title | Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications |
| title_full | Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications |
| title_fullStr | Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications |
| title_full_unstemmed | Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications |
| title_short | Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications |
| title_sort | integral inequalities of integer and fractional orders for n polynomial harmonically tgs convex functions and their applications |
| url | http://dx.doi.org/10.1155/2022/2493944 |
| work_keys_str_mv | AT artionkashuri integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT soubhagyakumarsahoo integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT bibhakarkodamasingh integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT muhammadtariq integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT ahmedahamoud integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT homanemadifar integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT faraidunkhamasalh integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT nedalmmohammed integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications AT masoumehkhademi integralinequalitiesofintegerandfractionalordersfornpolynomialharmonicallytgsconvexfunctionsandtheirapplications |