On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals
This article investigates inequalities for certain types of strongly convex functions by applying <i>q</i>-<i>h</i>-integrals. These inequalities provide the refinements of some well-known results that hold for <inline-formula><math display="inline"><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/10/705 |
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| author | Ghulam Farid Wajida Akram Ferdous M. O. Tawfiq Jong-Suk Ro Fairouz Tchier Saira Zainab |
| author_facet | Ghulam Farid Wajida Akram Ferdous M. O. Tawfiq Jong-Suk Ro Fairouz Tchier Saira Zainab |
| author_sort | Ghulam Farid |
| collection | DOAJ |
| description | This article investigates inequalities for certain types of strongly convex functions by applying <i>q</i>-<i>h</i>-integrals. These inequalities provide the refinements of some well-known results that hold for <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>- and <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mo>ℏ</mo></mrow></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mrow><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex and related functions. Inequalities for <i>q</i>-integrals are deducible by vanishing the parameter <i>h</i>. Some particular cases are discussed after proving the main results. |
| first_indexed | 2024-03-10T21:15:07Z |
| format | Article |
| id | doaj.art-d95285892dca488f93d96a79219934b4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T21:15:07Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d95285892dca488f93d96a79219934b42023-11-19T16:34:05ZengMDPI AGFractal and Fractional2504-31102023-09-0171070510.3390/fractalfract7100705On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-IntegralsGhulam Farid0Wajida Akram1Ferdous M. O. Tawfiq2Jong-Suk Ro3Fairouz Tchier4Saira Zainab5Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, PakistanDepartment of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, PakistanDepartment of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi ArabiaSchool of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of KoreaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi ArabiaSchool of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, PakistanThis article investigates inequalities for certain types of strongly convex functions by applying <i>q</i>-<i>h</i>-integrals. These inequalities provide the refinements of some well-known results that hold for <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>- and <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mo>ℏ</mo></mrow></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mrow><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex and related functions. Inequalities for <i>q</i>-integrals are deducible by vanishing the parameter <i>h</i>. Some particular cases are discussed after proving the main results.https://www.mdpi.com/2504-3110/7/10/705<i>q</i>-derivative/integral<i>q</i>-<i>h</i>-derivative/integralconvex functionstrongly convex functionHermite–Hadamard inequality |
| spellingShingle | Ghulam Farid Wajida Akram Ferdous M. O. Tawfiq Jong-Suk Ro Fairouz Tchier Saira Zainab On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals Fractal and Fractional <i>q</i>-derivative/integral <i>q</i>-<i>h</i>-derivative/integral convex function strongly convex function Hermite–Hadamard inequality |
| title | On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals |
| title_full | On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals |
| title_fullStr | On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals |
| title_full_unstemmed | On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals |
| title_short | On Certain Inequalities for Several Kinds of Strongly Convex Functions for <em>q</em>-<em>h</em>-Integrals |
| title_sort | on certain inequalities for several kinds of strongly convex functions for em q em em h em integrals |
| topic | <i>q</i>-derivative/integral <i>q</i>-<i>h</i>-derivative/integral convex function strongly convex function Hermite–Hadamard inequality |
| url | https://www.mdpi.com/2504-3110/7/10/705 |
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