Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions
In this work, we introduce the idea of n–polynomial harmonically s–type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are es...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6615948 |
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| _version_ | 1832563185858641920 |
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| author | Saad Ihsan Butt Saima Rashid Muhammad Tariq Miao-Kun Wang |
| author_facet | Saad Ihsan Butt Saima Rashid Muhammad Tariq Miao-Kun Wang |
| author_sort | Saad Ihsan Butt |
| collection | DOAJ |
| description | In this work, we introduce the idea of n–polynomial harmonically s–type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers). |
| format | Article |
| id | doaj-art-e57fea50170a42008a055c9cec7e2624 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e57fea50170a42008a055c9cec7e26242025-02-03T01:20:51ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66159486615948Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special FunctionsSaad Ihsan Butt0Saima Rashid1Muhammad Tariq2Miao-Kun Wang3COMSATS University Islamabad, Lahore Campus, PakistanDepartment of Mathematics, Government College University, Faisalabad 38000, PakistanCOMSATS University Islamabad, Lahore Campus, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaIn this work, we introduce the idea of n–polynomial harmonically s–type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).http://dx.doi.org/10.1155/2021/6615948 |
| spellingShingle | Saad Ihsan Butt Saima Rashid Muhammad Tariq Miao-Kun Wang Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions Journal of Function Spaces |
| title | Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions |
| title_full | Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions |
| title_fullStr | Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions |
| title_full_unstemmed | Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions |
| title_short | Novel Refinements via n–Polynomial Harmonically s–Type Convex Functions and Application in Special Functions |
| title_sort | novel refinements via n polynomial harmonically s type convex functions and application in special functions |
| url | http://dx.doi.org/10.1155/2021/6615948 |
| work_keys_str_mv | AT saadihsanbutt novelrefinementsvianpolynomialharmonicallystypeconvexfunctionsandapplicationinspecialfunctions AT saimarashid novelrefinementsvianpolynomialharmonicallystypeconvexfunctionsandapplicationinspecialfunctions AT muhammadtariq novelrefinementsvianpolynomialharmonicallystypeconvexfunctionsandapplicationinspecialfunctions AT miaokunwang novelrefinementsvianpolynomialharmonicallystypeconvexfunctionsandapplicationinspecialfunctions |