Compactness result and its applications in integral equations

被引：4

作者：

Krukowski, Mateusz ^{[1
]}

Przeradzki, Bogdan ^{[1
]}

机构：

[1] Lodz Univ Technol, Inst Math, Wolczanska 215, PL-90924 Lodz, Poland

来源：

JOURNAL OF APPLIED ANALYSIS | 2016年 / 22卷 / 02期

关键词：

Arzela-Ascoli theorem; compact operators; Fredholm; Hammerstein; Urysohn;

D O I：

10.1515/jaa-2016-0016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A version of the Arzela-Ascoli theorem for X being a sigma-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem.

引用

页码：153 / 161

页数：9

共 50 条

[1] AN EXISTENCE RESULT FOR A CLASS OF NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS
Latrach, Khalid
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2015, 27 (02) : 199 - 218
[2] An existence result with numerical solution of nonlinear fractional integral equations
Kazemi, Manochehr
Deep, Amar
Nieto, Juan
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (09) : 10384 - 10399
[3] Dominated Compactness Theorem in Banach Function Spaces and its Applications
Humberto Rafeiro
Stefan Samko
Complex Analysis and Operator Theory, 2008, 2 : 669 - 681
[4] Dominated Compactness Theorem in Banach Function Spaces and its Applications
Rafeiro, Humberto
Samko, Stefan
COMPLEX ANALYSIS AND OPERATOR THEORY, 2008, 2 (04) : 669 - 681
[5] Delta basis functions and their applications to systems of integral equations
Roodaki, M.
Almasieh, H.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (01) : 100 - 109
[6] Positive solutions for a system of nonlinear Hammerstein integral equations and applications
Yang, Zhilin
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (22) : 11138 - 11150
[7] On measure of noncompactness in variable exponent Lebesgue spaces and applications to integral equations
Metwali, Mohamed M. A.
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2023, 2023 (01)
[8] Characterization of Compactness of the Commutators of Bilinear Fractional Integral Operators
Chaffee, Lucas
Torres, Rodolfo H.
POTENTIAL ANALYSIS, 2015, 43 (03) : 481 - 494
[9] CHARACTERIZATION OF COMPACTNESS OF COMMUTATORS OF BILINEAR SINGULAR INTEGRAL OPERATORS
Chaffee, Lucas
Chen, Peng
Han, Yanchang
Torres, Rodolfo H.
Ward, Lesley A.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (09) : 3943 - 3953
[10] Characterization of Compactness of the Commutators of Bilinear Fractional Integral Operators
Lucas Chaffee
Rodolfo H. Torres
Potential Analysis, 2015, 43 : 481 - 494

← 1 2 3 4 5 →