Generalization of hermite-hadamard type inequalities and their applications
This thesis is concerned with the study of generalization, refinement, improvement and extension of Hermite-Hadamard (H-H) type inequalities. These are achieved by using various classes of convex functions and different fractional integrals. We established new integral inequalities of H-H type vi...
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| Format: | Thesis |
| Language: | English |
| Published: |
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf |
| _version_ | 1796982782023434240 |
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| author | Almutairi, Ohud Bulayhan |
| author_facet | Almutairi, Ohud Bulayhan |
| author_sort | Almutairi, Ohud Bulayhan |
| collection | UPM |
| description | This thesis is concerned with the study of generalization, refinement, improvement
and extension of Hermite-Hadamard (H-H) type inequalities. These are achieved by
using various classes of convex functions and different fractional integrals. We established
new integral inequalities of H-H type via s-convex functions in the second
sense, as well as the new classes of convexities: h-Godunova-Levin and h-Godunova-
Levin preinvex functions. We also generalized the inequalities of the H-H type involving
Riemann-Liouville via generalized s-convex functions in the second sense
on fractal sets. We further generalized the H-H type inequalities involving Katugampola
fractional integrals via different types of convexities. We also improved several
inequalities of H-H type through various classes of convexities by using the conditions
| g' |q and | g" |q for q ≥ 1. Using the obtained new results, we presented
some applications to special means and applications to numerical integration. By
comparing the error bounds estimation of numerical integrations, report shows that
the present results obtained using generalization of mid-point and trapezoid type inequalities
are more efficient. Several quadrature rules were reported to be examined
through this approach. The findings of this study are new, more general and to some
extend better than many other research results. |
| first_indexed | 2024-03-06T10:56:56Z |
| format | Thesis |
| id | upm.eprints-92721 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:56:56Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | upm.eprints-927212022-04-21T01:19:05Z http://psasir.upm.edu.my/id/eprint/92721/ Generalization of hermite-hadamard type inequalities and their applications Almutairi, Ohud Bulayhan This thesis is concerned with the study of generalization, refinement, improvement and extension of Hermite-Hadamard (H-H) type inequalities. These are achieved by using various classes of convex functions and different fractional integrals. We established new integral inequalities of H-H type via s-convex functions in the second sense, as well as the new classes of convexities: h-Godunova-Levin and h-Godunova- Levin preinvex functions. We also generalized the inequalities of the H-H type involving Riemann-Liouville via generalized s-convex functions in the second sense on fractal sets. We further generalized the H-H type inequalities involving Katugampola fractional integrals via different types of convexities. We also improved several inequalities of H-H type through various classes of convexities by using the conditions | g' |q and | g" |q for q ≥ 1. Using the obtained new results, we presented some applications to special means and applications to numerical integration. By comparing the error bounds estimation of numerical integrations, report shows that the present results obtained using generalization of mid-point and trapezoid type inequalities are more efficient. Several quadrature rules were reported to be examined through this approach. The findings of this study are new, more general and to some extend better than many other research results. 2020-12 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf Almutairi, Ohud Bulayhan (2020) Generalization of hermite-hadamard type inequalities and their applications. Doctoral thesis, Universiti Putra Malaysia. Hadamard matrices Combinatorial analysis |
| spellingShingle | Hadamard matrices Combinatorial analysis Almutairi, Ohud Bulayhan Generalization of hermite-hadamard type inequalities and their applications |
| title | Generalization of hermite-hadamard type inequalities and their applications |
| title_full | Generalization of hermite-hadamard type inequalities and their applications |
| title_fullStr | Generalization of hermite-hadamard type inequalities and their applications |
| title_full_unstemmed | Generalization of hermite-hadamard type inequalities and their applications |
| title_short | Generalization of hermite-hadamard type inequalities and their applications |
| title_sort | generalization of hermite hadamard type inequalities and their applications |
| topic | Hadamard matrices Combinatorial analysis |
| url | http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf |
| work_keys_str_mv | AT almutairiohudbulayhan generalizationofhermitehadamardtypeinequalitiesandtheirapplications |