Global Bounds for the Generalized Jensen Functional with Applications

In this article we give sharp global bounds for the generalized Jensen functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>n</mi></msub><mr...

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Autores principales:	Slavko Simić, Bandar Bin-Mohsin
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Jensen functional A-G-H inequalities global bounds power means convex functions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a2c0c3c2e0ee4ffeb51ad8fdd8335796
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spelling	oai:doaj.org-article:a2c0c3c2e0ee4ffeb51ad8fdd83357962021-11-25T19:06:47ZGlobal Bounds for the Generalized Jensen Functional with Applications10.3390/sym131121052073-8994https://doaj.org/article/a2c0c3c2e0ee4ffeb51ad8fdd83357962021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2105https://doaj.org/toc/2073-8994In this article we give sharp global bounds for the generalized Jensen functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>n</mi></msub><mrow><mo stretchy="false">(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>;</mo><mi mathvariant="bold">p</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means.Slavko SimićBandar Bin-MohsinMDPI AGarticleJensen functionalA-G-H inequalitiesglobal boundspower meansconvex functionsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2105, p 2105 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Jensen functional A-G-H inequalities global bounds power means convex functions Mathematics QA1-939
spellingShingle	Jensen functional A-G-H inequalities global bounds power means convex functions Mathematics QA1-939 Slavko Simić Bandar Bin-Mohsin Global Bounds for the Generalized Jensen Functional with Applications
description	In this article we give sharp global bounds for the generalized Jensen functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>n</mi></msub><mrow><mo stretchy="false">(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>;</mo><mi mathvariant="bold">p</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means.
format	article
author	Slavko Simić Bandar Bin-Mohsin
author_facet	Slavko Simić Bandar Bin-Mohsin
author_sort	Slavko Simić
title	Global Bounds for the Generalized Jensen Functional with Applications
title_short	Global Bounds for the Generalized Jensen Functional with Applications
title_full	Global Bounds for the Generalized Jensen Functional with Applications
title_fullStr	Global Bounds for the Generalized Jensen Functional with Applications
title_full_unstemmed	Global Bounds for the Generalized Jensen Functional with Applications
title_sort	global bounds for the generalized jensen functional with applications
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a2c0c3c2e0ee4ffeb51ad8fdd8335796
work_keys_str_mv	AT slavkosimic globalboundsforthegeneralizedjensenfunctionalwithapplications AT bandarbinmohsin globalboundsforthegeneralizedjensenfunctionalwithapplications
_version_	1718410295719755776

Global Bounds for the Generalized Jensen Functional with Applications

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