On bounds involving k-Appell’s hypergeometric functions
Abstract In this paper, we derive a new extension of Hermite-Hadamard’s inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appe...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-05-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1391-2 |
| _version_ | 1818206239133270016 |
|---|---|
| author | Muhammad Uzair Awan Muhammad Aslam Noor Marcela V Mihai Khalida Inayat Noor |
| author_facet | Muhammad Uzair Awan Muhammad Aslam Noor Marcela V Mihai Khalida Inayat Noor |
| author_sort | Muhammad Uzair Awan |
| collection | DOAJ |
| description | Abstract In this paper, we derive a new extension of Hermite-Hadamard’s inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell’s hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal and mid-point type inequalities. These results are obtained for the functions which have the harmonic convexity property. We also discuss some special cases which can be deduced from the main results of the paper. |
| first_indexed | 2024-12-12T04:09:52Z |
| format | Article |
| id | doaj.art-d790cb833b5a4272a99adae060c243aa |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-12T04:09:52Z |
| publishDate | 2017-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d790cb833b5a4272a99adae060c243aa2022-12-22T00:38:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-05-012017111510.1186/s13660-017-1391-2On bounds involving k-Appell’s hypergeometric functionsMuhammad Uzair Awan0Muhammad Aslam Noor1Marcela V Mihai2Khalida Inayat Noor3Department of Mathematics, Government College UniversityDepartment of Mathematics, King Saud UniversityDepartment scientific-methodical sessions, Romanian Mathematical Society-branch BucharestDepartment of Mathematics, COMSATS Institute of Information TechnologyAbstract In this paper, we derive a new extension of Hermite-Hadamard’s inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell’s hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal and mid-point type inequalities. These results are obtained for the functions which have the harmonic convexity property. We also discuss some special cases which can be deduced from the main results of the paper.http://link.springer.com/article/10.1186/s13660-017-1391-2convex functionsharmonic convex functionsk-fractionalk-Appell’s hypergeometric functionsinequalities |
| spellingShingle | Muhammad Uzair Awan Muhammad Aslam Noor Marcela V Mihai Khalida Inayat Noor On bounds involving k-Appell’s hypergeometric functions Journal of Inequalities and Applications convex functions harmonic convex functions k-fractional k-Appell’s hypergeometric functions inequalities |
| title | On bounds involving k-Appell’s hypergeometric functions |
| title_full | On bounds involving k-Appell’s hypergeometric functions |
| title_fullStr | On bounds involving k-Appell’s hypergeometric functions |
| title_full_unstemmed | On bounds involving k-Appell’s hypergeometric functions |
| title_short | On bounds involving k-Appell’s hypergeometric functions |
| title_sort | on bounds involving k appell s hypergeometric functions |
| topic | convex functions harmonic convex functions k-fractional k-Appell’s hypergeometric functions inequalities |
| url | http://link.springer.com/article/10.1186/s13660-017-1391-2 |
| work_keys_str_mv | AT muhammaduzairawan onboundsinvolvingkappellshypergeometricfunctions AT muhammadaslamnoor onboundsinvolvingkappellshypergeometricfunctions AT marcelavmihai onboundsinvolvingkappellshypergeometricfunctions AT khalidainayatnoor onboundsinvolvingkappellshypergeometricfunctions |