Compactness result and its applications in integral equations
-
Mateusz Krukowski
und
Bogdan Przeradzki
Abstract
A version of the Arzelà–Ascoli theorem for X being a σ-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.
Acknowledgements
We would like to express our utmost gratitude to both referees for all comments and suggestions. The paper has benefited tremendously from all their remarks. With pleasure, we acknowledge the contribution of the referees.
References
[1] Benedetto J. J. and Czaja W., Integration and Modern Analysis, Birkhäuser, Boston, 2009. 10.1007/978-0-8176-4656-1Suche in Google Scholar
[2] Corduneanu C., Integral Equations and Applications, Cambridge University Press, Cambridge, 1991. 10.1017/CBO9780511569395Suche in Google Scholar
[3] Engelking R., General Topology, Polish Scientific Publishers, Warsaw, 1997. Suche in Google Scholar
[4] Kołodziej W., Wybrane rozdziały analizy matematycznej, Polish Scientific Publishers, Warsaw, 1982. Suche in Google Scholar
[5] Krasnosielskii M. A., Zabreiko P. P., Pustylnik E. I. and Sbolevskii P. E., Integral Operators in Spaces of Summable Functions, Noordhoff International Publishing, Leyden, 1976. 10.1007/978-94-010-1542-4Suche in Google Scholar
[6] Munkres J. R., Topology, Prentice Hall, Upper Saddle River, 2000. Suche in Google Scholar
[7] Porter D. and Stirling D. S. G., Integral Equations. A Practical Treatment, from Spectral Theory to Applications, Cambridge University Press, Cambridge, 1990. 10.1017/CBO9781139172028Suche in Google Scholar
[8] Przeradzki B., The existence of bounded solutions for differential equations in Hilbert spaces, Ann. Polon. Math. 56 (1992), no. 2, 103–121. 10.4064/ap-56-2-103-121Suche in Google Scholar
[9] Stańczy R., Hammerstein equation with an integral over noncompact domain, Ann. Polon. Math. 69 (1998), no. 1, 49–60. 10.4064/ap-69-1-49-60Suche in Google Scholar
[10] Zemyan S. M., The Classical Theory of Integral Equations, Birkhäuser, New York, 2012. 10.1007/978-0-8176-8349-8Suche in Google Scholar
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- On the cubic and cubic-quintic optical vortices equations
- Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation
- Simultaneously proximinal subspaces
- Iteration regularized semigroups of set-valued functions
- A recursive-operational approach with applications to linear differential systems
- On symmetrically porouscontinuous functions
- Compactness result and its applications in integral equations
-
On statistically
- Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem
Artikel in diesem Heft
- Frontmatter
- On the cubic and cubic-quintic optical vortices equations
- Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation
- Simultaneously proximinal subspaces
- Iteration regularized semigroups of set-valued functions
- A recursive-operational approach with applications to linear differential systems
- On symmetrically porouscontinuous functions
- Compactness result and its applications in integral equations
-
On statistically
- Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem
