Existence and uniqueness of fixed points of an integral operator of Hammerstein type
type: Item
instance of: scholarly article
title: Existence and uniqueness of fixed points of an integral operator of Hammerstein type
zbMATH Open document ID: 1490.45014
DOI: 10.1134/S0040577921090051
published in: Theoretical and Mathematical Physics
publication date: 2021-12-08T00:00:00Z
review text: The author discusses the fixed points of a nonlinear integral operator of Hammerstein type. Here, such an operator is neither compact nor contracting. Therefore, some well-known theorems such as the Schauder fixed-point theorem and the Banach fixed-point theorem do not apply. The existence of fixed points of nonlinear integral operators of Hammerstein type has been established by other authors, and the author of the present paper establishes their uniqueness under certain conditions. Moreover, he applies the results to several interesting examples such as the antiferromagnetic and ferromagnetic Ising models.
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7440668
zbMATH Keywords: Hammerstein integral operator
zbMATH Keywords: positive fixed point
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: cone
zbMATH Keywords: normal cone
author: Farhod Halimjonovich Haydarov
reviewed by: Shuji Watanabe
MaRDI profile type: Publication
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full work available at URL: s0040577921090051
OpenAlex ID: W3203006382
description: scientific article; zbMATH DE number 7440668