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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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第一著者: Almutairi, Ohud Bulayhan
フォーマット: 学位論文
言語:English
出版事項: 2020
主題:
Hadamard matrices
Combinatorial analysis
オンライン･アクセス:http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf
http://psasir.upm.edu.my/id/eprint/92721/
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spelling my.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
topic Hadamard matrices
Combinatorial analysis
spellingShingle Hadamard matrices
Combinatorial analysis
Almutairi, Ohud Bulayhan
Generalization of hermite-hadamard type inequalities and their applications
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.
format Thesis
author Almutairi, Ohud Bulayhan
author_facet Almutairi, Ohud Bulayhan
author_sort Almutairi, Ohud Bulayhan
title Generalization of hermite-hadamard type inequalities and their applications
title_short 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_sort generalization of hermite-hadamard type inequalities and their applications
publishDate 2020
url http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf
http://psasir.upm.edu.my/id/eprint/92721/
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score 13.250246

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