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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Main Author:	Almutairi, Ohud Bulayhan
Format:	Thesis
Language:	English
Published:	2020
Subjects:	Hadamard matrices Combinatorial analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf
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id	my-upm-ir.92721
record_format	uketd_dc
spelling	my-upm-ir.927212022-04-21T01:19:05Z Generalization of hermite-hadamard type inequalities and their applications 2020-12 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. Hadamard matrices Combinatorial analysis 2020-12 Thesis http://psasir.upm.edu.my/id/eprint/92721/ http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf text en public doctoral Universiti Putra Malaysia Hadamard matrices Combinatorial analysis Kilicman, Adem
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Kilicman, Adem
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
qualification_level	Doctorate
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
granting_institution	Universiti Putra Malaysia
publishDate	2020
url	http://psasir.upm.edu.my/id/eprint/92721/1/FS%202021%208%20-IR.pdf
_version_	1747813756192161792

Generalization of hermite-hadamard type inequalities and their applications

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