BourbakiV1, Main, Exploration, bibRecord, 000004

New applications of the existence of solutions for equilibrium equations with Neumann type boundary condition

Identifieur interne : 000004 ( Main/Exploration ); précédent : 000003; suivant : 000005

New applications of the existence of solutions for equilibrium equations with Neumann type boundary condition

Auteurs : Zhaoqi Ji [République populaire de Chine] ; Tao Liu [République populaire de Chine] ; Hong Tian [République populaire de Chine] ; Tanriver Ülker

Source :

Journal of Inequalities and Applications [ 1025-5834 ] ; 2017.

RBID : PMC:5400806

Abstract

Using the existence of solutions for equilibrium equations with a Neumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl. 2015:363, 2015), we obtain the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space, which are generalizations of integral representations for harmonic functions proved by Leng, Xu and Zhao (Comput. Math. Appl. 66:1-18, 2013). We also deduce the Riesz integral representation for set-valued maps, for the vector-valued maps of Diestel-Uhl and for the scalar-valued maps of Dunford-Schwartz.

Url:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5400806

DOI: 10.1186/s13660-017-1357-4
PubMed: 28490851
PubMed Central: 5400806

Affiliations:

République populaire de Chine

Le document en format XML

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<front><div type="abstract" xml:lang="en"><p>Using the existence of solutions for equilibrium equations with a Neumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl. 2015:363, <xref ref-type="bibr" rid="CR1">2015</xref>
), we obtain the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space, which are generalizations of integral representations for harmonic functions proved by Leng, Xu and Zhao (Comput. Math. Appl. 66:1-18, <xref ref-type="bibr" rid="CR2">2013</xref>
). We also deduce the Riesz integral representation for set-valued maps, for the vector-valued maps of Diestel-Uhl and for the scalar-valued maps of Dunford-Schwartz.</p>
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New applications of the existence of solutions for equilibrium equations with Neumann type boundary condition

New applications of the existence of solutions for equilibrium equations with Neumann type boundary condition

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