Some new integral inequalities for (s, m)-convex and (α, m)-convex functions
The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are ( s,m )-convex and ( α,m )-convex functions. These results are related to well - known Hermite-Hadamard type integral inequality, Simpson type integral inequa...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2019-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/253 |
| _version_ | 1827395692183683072 |
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| author | B. Bayraktar V.Ch. Kudaev |
| author_facet | B. Bayraktar V.Ch. Kudaev |
| author_sort | B. Bayraktar |
| collection | DOAJ |
| description |
The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are ( s,m )-convex and ( α,m )-convex functions. These results are related to well - known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensen type inequality. In other words, new upper bounds for these inequalities using the indicated classes of convex functions have been obtained. These estimates are obtained using a direct definition for a convex function, classical integral inequalities of Ho¨lder and power mean types. Along with the new outcomes, the paper presents results confirming the existing in literature upper bound estimates for integral inequalities (in particular well known in literature results obtained by U. Kırmacı in [7] and M.Z. Sarıkaya and N. Aktan in [35]). The last section presents some applications of the obtained estimates for special computing facilities (arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities).
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| first_indexed | 2024-03-08T18:39:24Z |
| format | Article |
| id | doaj.art-e1af4cbdb30d4a01bd6eb2e8e4230758 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:24Z |
| publishDate | 2019-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-e1af4cbdb30d4a01bd6eb2e8e42307582023-12-29T10:20:54ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-06-0194210.31489/2019m2/15-25Some new integral inequalities for (s, m)-convex and (α, m)-convex functionsB. BayraktarV.Ch. Kudaev The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are ( s,m )-convex and ( α,m )-convex functions. These results are related to well - known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensen type inequality. In other words, new upper bounds for these inequalities using the indicated classes of convex functions have been obtained. These estimates are obtained using a direct definition for a convex function, classical integral inequalities of Ho¨lder and power mean types. Along with the new outcomes, the paper presents results confirming the existing in literature upper bound estimates for integral inequalities (in particular well known in literature results obtained by U. Kırmacı in [7] and M.Z. Sarıkaya and N. Aktan in [35]). The last section presents some applications of the obtained estimates for special computing facilities (arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities). http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/253convex function(s, m)-convex(α, m)-convexHermite–Hadamard inequalitiyH¨older inequalitypower mean inequality |
| spellingShingle | B. Bayraktar V.Ch. Kudaev Some new integral inequalities for (s, m)-convex and (α, m)-convex functions Қарағанды университетінің хабаршысы. Математика сериясы convex function (s, m)-convex (α, m)-convex Hermite–Hadamard inequalitiy H¨older inequality power mean inequality |
| title | Some new integral inequalities for (s, m)-convex and (α, m)-convex functions |
| title_full | Some new integral inequalities for (s, m)-convex and (α, m)-convex functions |
| title_fullStr | Some new integral inequalities for (s, m)-convex and (α, m)-convex functions |
| title_full_unstemmed | Some new integral inequalities for (s, m)-convex and (α, m)-convex functions |
| title_short | Some new integral inequalities for (s, m)-convex and (α, m)-convex functions |
| title_sort | some new integral inequalities for s m convex and α m convex functions |
| topic | convex function (s, m)-convex (α, m)-convex Hermite–Hadamard inequalitiy H¨older inequality power mean inequality |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/253 |
| work_keys_str_mv | AT bbayraktar somenewintegralinequalitiesforsmconvexandamconvexfunctions AT vchkudaev somenewintegralinequalitiesforsmconvexandamconvexfunctions |