Perturbation of a single-valued operator by a multi-valued mapping of Hammerstein type with nonconvex images
type: Item
instance of: scholarly article
title: Perturbation of a single-valued operator by a multi-valued mapping of Hammerstein type with nonconvex images
zbMATH Open document ID: 0999.47035
author: L. I. Tkach
author: Aleksander Bulgakov
published in: Russian Mathematics
publication date: 2001-03-07T00:00:00Z
review text: The authors study the inclusion \(x\in f(x)+ V\Phi(x)\), where \(f: C([a,b],\mathbb{R}^n)\to C([a,b],\mathbb{R}^n)\) is compact, \(\Phi: C([a,b],\mathbb{R}^n)\to L^1([a,b],\mathbb{R}^n)\) is multivalued with certain additional properties, and \(V: L^1([a,b],\mathbb{R}^n)\to C([a,b],\mathbb{R}^n)\) is a linear integral operator. The main tool is a fixed point result due to the first author [Mat. Sb. 183, No. 10, 63-86 (1992; Zbl 0772.34017)].
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1541446
zbMATH Keywords: inclusion
zbMATH Keywords: linear integral operator
reviewed by: Jürgen Appell
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541446