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Title: Convexity properties of images under nonlinear integral operators

Abstract

Conditions are obtained for the image of a given set under a general completely continuous nonlinear integral operator to have convex closure. These results are used to establish the uniqueness of quasi-solutions of nonlinear integral equations of the first kind and to prove the solvability of equations of the first kind on a dense subset of the right-hand sides. Bibliography: 11 titles.

Authors:
 [1]
  1. Mari State Technical University, Ioshkar-Ola (Russian Federation)
Publication Date:
OSTI Identifier:
22364158
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 205; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; IMAGES; INTEGRAL EQUATIONS; INTEGRALS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS

Citation Formats

Kokurin, M Yu. Convexity properties of images under nonlinear integral operators. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N12ABEH004439.
Kokurin, M Yu. Convexity properties of images under nonlinear integral operators. United States. https://doi.org/10.1070/SM2014V205N12ABEH004439
Kokurin, M Yu. 2014. "Convexity properties of images under nonlinear integral operators". United States. https://doi.org/10.1070/SM2014V205N12ABEH004439.
@article{osti_22364158,
title = {Convexity properties of images under nonlinear integral operators},
author = {Kokurin, M Yu},
abstractNote = {Conditions are obtained for the image of a given set under a general completely continuous nonlinear integral operator to have convex closure. These results are used to establish the uniqueness of quasi-solutions of nonlinear integral equations of the first kind and to prove the solvability of equations of the first kind on a dense subset of the right-hand sides. Bibliography: 11 titles.},
doi = {10.1070/SM2014V205N12ABEH004439},
url = {https://www.osti.gov/biblio/22364158}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 12,
volume = 205,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 2014},
month = {Wed Dec 31 00:00:00 EST 2014}
}