Abstract Volterra operators
type: Item
instance of: scholarly article
title: Abstract Volterra operators
zbMATH Open document ID: 1172.47041
DOI: 10.3103/S1066369X08030018
author: J. Martínez
published in: Russian Mathematics
publication date: 2009-03-26T00:00:00Z
review text: The paper is concerned with a new definition of Volterra operators that generalizes A.\,N.\thinspace Tikhonov's classical formulation. The properties of Volterra operators on arbitrary sets are first discussed, followed by an analysis of Volterra operators in Banach spaces. In particular, the authors study the solvability of nonlinear equations with generalized Volterra operators. As an application, a functional-differential equation is considered.
reviewed by: Sergiu Aizicovici
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5533457
zbMATH Keywords: abstract Volterra operators
zbMATH Keywords: Volterra invertibility of operators
zbMATH Keywords: local solutions
zbMATH Keywords: extension of solutions
zbMATH Keywords: uniqueness of a solution
zbMATH Keywords: functional differential equations
MaRDI profile type: Publication
cites work: Q3833033
cites work: Measures of noncompactness and condensing operators. Transl. from the Russian by A. Iacob
cites work: Q3218622
cites work: Q3996831
cites work: Q4466920
description: scientific article; zbMATH DE number 5533457