Integral Inequalities Involving Strongly Convex Functions
We study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptur...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6595921 |
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| _version_ | 1849396577160921088 |
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| author | Ying-Qing Song Muhammad Adil Khan Syed Zaheer Ullah Yu-Ming Chu |
| author_facet | Ying-Qing Song Muhammad Adil Khan Syed Zaheer Ullah Yu-Ming Chu |
| author_sort | Ying-Qing Song |
| collection | DOAJ |
| description | We study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater’s inequality for strongly convex functions. |
| format | Article |
| id | doaj-art-afdb79d1c0f94f59ae2e52d10bd61fb1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-afdb79d1c0f94f59ae2e52d10bd61fb12025-08-20T03:39:18ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/65959216595921Integral Inequalities Involving Strongly Convex FunctionsYing-Qing Song0Muhammad Adil Khan1Syed Zaheer Ullah2Yu-Ming Chu3College of Science, Hunan City University, Yiyang 413000, ChinaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaWe study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater’s inequality for strongly convex functions.http://dx.doi.org/10.1155/2018/6595921 |
| spellingShingle | Ying-Qing Song Muhammad Adil Khan Syed Zaheer Ullah Yu-Ming Chu Integral Inequalities Involving Strongly Convex Functions Journal of Function Spaces |
| title | Integral Inequalities Involving Strongly Convex Functions |
| title_full | Integral Inequalities Involving Strongly Convex Functions |
| title_fullStr | Integral Inequalities Involving Strongly Convex Functions |
| title_full_unstemmed | Integral Inequalities Involving Strongly Convex Functions |
| title_short | Integral Inequalities Involving Strongly Convex Functions |
| title_sort | integral inequalities involving strongly convex functions |
| url | http://dx.doi.org/10.1155/2018/6595921 |
| work_keys_str_mv | AT yingqingsong integralinequalitiesinvolvingstronglyconvexfunctions AT muhammadadilkhan integralinequalitiesinvolvingstronglyconvexfunctions AT syedzaheerullah integralinequalitiesinvolvingstronglyconvexfunctions AT yumingchu integralinequalitiesinvolvingstronglyconvexfunctions |